id	sid	tid	token	lemma	pos
ejpam-3363	1	1	a	a	DET
ejpam-3363	1	2	descriptive	descriptive	ADJ
ejpam-3363	1	3	definition	definition	NOUN
ejpam-3363	1	4	of	of	ADP
ejpam-3363	1	5	the	the	DET
ejpam-3363	1	6	ito	ito	PROPN
ejpam-3363	1	7	-	-	PUNCT
ejpam-3363	1	8	mcshane	mcshane	PROPN
ejpam-3363	1	9	integral	integral	ADJ
ejpam-3363	1	10	for	for	ADP
ejpam-3363	1	11	the	the	DET
ejpam-3363	1	12	hilbert	hilbert	NOUN
ejpam-3363	1	13	-	-	PUNCT
ejpam-3363	1	14	schmidt	schmidt	VERB
ejpam-3363	1	15	-	-	PUNCT
ejpam-3363	1	16	valued	value	VERB
ejpam-3363	1	17	stochastic	stochastic	ADJ
ejpam-3363	1	18	process	process	NOUN
ejpam-3363	1	19	european	european	ADJ
ejpam-3363	1	20	journal	journal	PROPN
ejpam-3363	1	21	of	of	ADP
ejpam-3363	1	22	pure	pure	ADJ
ejpam-3363	1	23	and	and	CCONJ
ejpam-3363	1	24	applied	apply	VERB
ejpam-3363	1	25	mathematics	mathematic	NOUN
ejpam-3363	1	26	vol	vol	NOUN
ejpam-3363	1	27	.	.	PROPN
ejpam-3363	2	1	12	12	NUM
ejpam-3363	2	2	,	,	PUNCT
ejpam-3363	2	3	no	no	INTJ
ejpam-3363	2	4	.	.	NOUN
ejpam-3363	2	5	1	1	NUM
ejpam-3363	2	6	,	,	PUNCT
ejpam-3363	2	7	2019	2019	NUM
ejpam-3363	2	8	,	,	PUNCT
ejpam-3363	2	9	101	101	NUM
ejpam-3363	2	10	-	-	SYM
ejpam-3363	2	11	117	117	NUM
ejpam-3363	2	12	issn	issn	PROPN
ejpam-3363	2	13	1307	1307	NUM
ejpam-3363	2	14	-	-	SYM
ejpam-3363	2	15	5543	5543	NUM
ejpam-3363	2	16	–	–	PUNCT
ejpam-3363	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3363	2	18	published	publish	VERB
ejpam-3363	2	19	by	by	ADP
ejpam-3363	2	20	new	new	PROPN
ejpam-3363	2	21	york	york	PROPN
ejpam-3363	2	22	business	business	PROPN
ejpam-3363	2	23	global	global	PROPN
ejpam-3363	2	24	a	a	DET
ejpam-3363	2	25	version	version	NOUN
ejpam-3363	2	26	of	of	ADP
ejpam-3363	2	27	fundamental	fundamental	ADJ
ejpam-3363	2	28	theorem	theorem	NOUN
ejpam-3363	2	29	for	for	ADP
ejpam-3363	2	30	the	the	DET
ejpam-3363	2	31	itô-mcshane	itô-mcshane	NOUN
ejpam-3363	2	32	integral	integral	ADJ
ejpam-3363	2	33	of	of	ADP
ejpam-3363	2	34	an	an	DET
ejpam-3363	2	35	operator	operator	NOUN
ejpam-3363	2	36	-	-	PUNCT
ejpam-3363	2	37	valued	value	VERB
ejpam-3363	2	38	stochastic	stochastic	NOUN
ejpam-3363	2	39	process	process	NOUN
ejpam-3363	2	40	jeffer	jeffer	VERB
ejpam-3363	2	41	dave	dave	PROPN
ejpam-3363	2	42	a.	a.	PROPN
ejpam-3363	2	43	cagubcob1	cagubcob1	PROPN
ejpam-3363	2	44	,	,	PUNCT
ejpam-3363	2	45	mhelmar	mhelmar	PROPN
ejpam-3363	2	46	a.	a.	PROPN
ejpam-3363	2	47	labendia1,∗	labendia1,∗	PROPN
ejpam-3363	2	48	1	1	NUM
ejpam-3363	2	49	department	department	NOUN
ejpam-3363	2	50	of	of	ADP
ejpam-3363	2	51	mathematics	mathematic	NOUN
ejpam-3363	2	52	and	and	CCONJ
ejpam-3363	2	53	statistics	statistic	NOUN
ejpam-3363	2	54	,	,	PUNCT
ejpam-3363	2	55	college	college	NOUN
ejpam-3363	2	56	of	of	ADP
ejpam-3363	2	57	science	science	NOUN
ejpam-3363	2	58	and	and	CCONJ
ejpam-3363	2	59	mathematics	mathematic	NOUN
ejpam-3363	2	60	,	,	PUNCT
ejpam-3363	2	61	mindanao	mindanao	PROPN
ejpam-3363	2	62	sate	sate	PROPN
ejpam-3363	2	63	university	university	PROPN
ejpam-3363	2	64	-	-	PUNCT
ejpam-3363	2	65	iligan	iligan	PROPN
ejpam-3363	2	66	institute	institute	PROPN
ejpam-3363	2	67	of	of	ADP
ejpam-3363	2	68	technology	technology	PROPN
ejpam-3363	2	69	,	,	PUNCT
ejpam-3363	2	70	9200	9200	NUM
ejpam-3363	2	71	iligan	iligan	ADJ
ejpam-3363	2	72	city	city	NOUN
ejpam-3363	2	73	,	,	PUNCT
ejpam-3363	2	74	philippines	philippine	NOUN
ejpam-3363	2	75	abstract	abstract	ADJ
ejpam-3363	2	76	.	.	PUNCT
ejpam-3363	3	1	in	in	ADP
ejpam-3363	3	2	this	this	DET
ejpam-3363	3	3	paper	paper	NOUN
ejpam-3363	3	4	,	,	PUNCT
ejpam-3363	3	5	we	we	PRON
ejpam-3363	3	6	formulate	formulate	VERB
ejpam-3363	3	7	a	a	DET
ejpam-3363	3	8	descriptive	descriptive	ADJ
ejpam-3363	3	9	definition	definition	NOUN
ejpam-3363	3	10	or	or	CCONJ
ejpam-3363	3	11	a	a	DET
ejpam-3363	3	12	version	version	NOUN
ejpam-3363	3	13	of	of	ADP
ejpam-3363	3	14	fundamental	fundamental	ADJ
ejpam-3363	3	15	theorem	theorem	NOUN
ejpam-3363	3	16	for	for	ADP
ejpam-3363	3	17	the	the	DET
ejpam-3363	3	18	itô-mcshane	itô-mcshane	NOUN
ejpam-3363	3	19	integral	integral	ADJ
ejpam-3363	3	20	of	of	ADP
ejpam-3363	3	21	an	an	DET
ejpam-3363	3	22	operator	operator	NOUN
ejpam-3363	3	23	-	-	PUNCT
ejpam-3363	3	24	valued	value	VERB
ejpam-3363	3	25	stochastic	stochastic	ADJ
ejpam-3363	3	26	process	process	NOUN
ejpam-3363	3	27	with	with	ADP
ejpam-3363	3	28	respect	respect	NOUN
ejpam-3363	3	29	to	to	ADP
ejpam-3363	3	30	a	a	DET
ejpam-3363	3	31	hilbert	hilbert	NOUN
ejpam-3363	3	32	space	space	NOUN
ejpam-3363	3	33	-	-	PUNCT
ejpam-3363	3	34	valued	value	VERB
ejpam-3363	3	35	wiener	wiener	NOUN
ejpam-3363	3	36	process	process	NOUN
ejpam-3363	3	37	.	.	PUNCT
ejpam-3363	4	1	for	for	ADP
ejpam-3363	4	2	this	this	DET
ejpam-3363	4	3	reason	reason	NOUN
ejpam-3363	4	4	,	,	PUNCT
ejpam-3363	4	5	we	we	PRON
ejpam-3363	4	6	introduce	introduce	VERB
ejpam-3363	4	7	the	the	DET
ejpam-3363	4	8	concept	concept	NOUN
ejpam-3363	4	9	of	of	ADP
ejpam-3363	4	10	belated	belate	VERB
ejpam-3363	4	11	mcshane	mcshane	PROPN
ejpam-3363	4	12	differentiability	differentiability	NOUN
ejpam-3363	4	13	and	and	CCONJ
ejpam-3363	4	14	a	a	DET
ejpam-3363	4	15	version	version	NOUN
ejpam-3363	4	16	of	of	ADP
ejpam-3363	4	17	absolute	absolute	ADJ
ejpam-3363	4	18	continuity	continuity	NOUN
ejpam-3363	4	19	of	of	ADP
ejpam-3363	4	20	a	a	DET
ejpam-3363	4	21	hilbert	hilbert	NOUN
ejpam-3363	4	22	space	space	NOUN
ejpam-3363	4	23	-	-	PUNCT
ejpam-3363	4	24	valued	value	VERB
ejpam-3363	4	25	stochastic	stochastic	ADJ
ejpam-3363	4	26	process	process	NOUN
ejpam-3363	4	27	.	.	PUNCT
ejpam-3363	5	1	2010	2010	NUM
ejpam-3363	5	2	mathematics	mathematic	NOUN
ejpam-3363	5	3	subject	subject	NOUN
ejpam-3363	5	4	classifications	classification	NOUN
ejpam-3363	5	5	:	:	PUNCT
ejpam-3363	5	6	60h30	60h30	NUM
ejpam-3363	5	7	,	,	PUNCT
ejpam-3363	5	8	60h05	60h05	NUM
ejpam-3363	5	9	key	key	ADJ
ejpam-3363	5	10	words	word	NOUN
ejpam-3363	5	11	and	and	CCONJ
ejpam-3363	5	12	phrases	phrase	NOUN
ejpam-3363	5	13	:	:	PUNCT
ejpam-3363	5	14	itô-mcshane	itô-mcshane	VERB
ejpam-3363	5	15	integral	integral	ADJ
ejpam-3363	5	16	,	,	PUNCT
ejpam-3363	5	17	orthogonal	orthogonal	ADJ
ejpam-3363	5	18	increment	increment	NOUN
ejpam-3363	5	19	property	property	NOUN
ejpam-3363	5	20	,	,	PUNCT
ejpam-3363	5	21	q	q	ADJ
ejpam-3363	5	22	-	-	PUNCT
ejpam-3363	5	23	wiener	wiener	NOUN
ejpam-3363	5	24	process	process	NOUN
ejpam-3363	5	25	,	,	PUNCT
ejpam-3363	5	26	ac2[0	ac2[0	PROPN
ejpam-3363	5	27	,	,	PUNCT
ejpam-3363	5	28	t	t	X
ejpam-3363	5	29	]	]	PUNCT
ejpam-3363	5	30	-property	-property	NOUN
ejpam-3363	5	31	1	1	NUM
ejpam-3363	5	32	.	.	PUNCT
ejpam-3363	5	33	introduction	introduction	NOUN
ejpam-3363	5	34	the	the	DET
ejpam-3363	5	35	henstock	henstock	NOUN
ejpam-3363	5	36	integral	integral	ADJ
ejpam-3363	5	37	,	,	PUNCT
ejpam-3363	5	38	which	which	PRON
ejpam-3363	5	39	was	be	AUX
ejpam-3363	5	40	studied	study	VERB
ejpam-3363	5	41	independently	independently	ADV
ejpam-3363	5	42	by	by	ADP
ejpam-3363	5	43	henstock	henstock	NOUN
ejpam-3363	5	44	and	and	CCONJ
ejpam-3363	5	45	kurzweil	kurzweil	PROPN
ejpam-3363	5	46	in	in	ADP
ejpam-3363	5	47	the	the	DET
ejpam-3363	5	48	1950s	1950	NOUN
ejpam-3363	5	49	and	and	CCONJ
ejpam-3363	5	50	later	later	ADV
ejpam-3363	5	51	known	know	VERB
ejpam-3363	5	52	as	as	ADP
ejpam-3363	5	53	the	the	DET
ejpam-3363	5	54	henstock	henstock	NOUN
ejpam-3363	5	55	-	-	PUNCT
ejpam-3363	5	56	kurzweil	kurzweil	PROPN
ejpam-3363	5	57	integral	integral	NOUN
ejpam-3363	5	58	,	,	PUNCT
ejpam-3363	5	59	is	be	AUX
ejpam-3363	5	60	one	one	NUM
ejpam-3363	5	61	of	of	ADP
ejpam-3363	5	62	the	the	DET
ejpam-3363	5	63	notable	notable	ADJ
ejpam-3363	5	64	integrals	integral	NOUN
ejpam-3363	5	65	that	that	PRON
ejpam-3363	5	66	was	be	AUX
ejpam-3363	5	67	introduced	introduce	VERB
ejpam-3363	5	68	which	which	PRON
ejpam-3363	5	69	in	in	ADP
ejpam-3363	5	70	some	some	DET
ejpam-3363	5	71	sense	sense	NOUN
ejpam-3363	5	72	is	be	AUX
ejpam-3363	5	73	more	more	ADV
ejpam-3363	5	74	general	general	ADJ
ejpam-3363	5	75	than	than	SCONJ
ejpam-3363	5	76	the	the	DET
ejpam-3363	5	77	lebesgue	lebesgue	NOUN
ejpam-3363	5	78	integral	integral	ADJ
ejpam-3363	5	79	.	.	PUNCT
ejpam-3363	6	1	to	to	PART
ejpam-3363	6	2	avoid	avoid	VERB
ejpam-3363	6	3	an	an	DET
ejpam-3363	6	4	extensive	extensive	ADJ
ejpam-3363	6	5	study	study	NOUN
ejpam-3363	6	6	of	of	ADP
ejpam-3363	6	7	measure	measure	NOUN
ejpam-3363	6	8	theory	theory	NOUN
ejpam-3363	6	9	,	,	PUNCT
ejpam-3363	6	10	henstock	henstock	NOUN
ejpam-3363	6	11	-	-	PUNCT
ejpam-3363	6	12	kurzweil	kurzweil	NOUN
ejpam-3363	6	13	integration	integration	NOUN
ejpam-3363	6	14	had	have	AUX
ejpam-3363	6	15	been	be	AUX
ejpam-3363	6	16	deeply	deeply	ADV
ejpam-3363	6	17	studied	study	VERB
ejpam-3363	6	18	and	and	CCONJ
ejpam-3363	6	19	investigated	investigate	VERB
ejpam-3363	6	20	by	by	ADP
ejpam-3363	6	21	numerous	numerous	ADJ
ejpam-3363	6	22	authors	author	NOUN
ejpam-3363	6	23	,	,	PUNCT
ejpam-3363	6	24	see	see	VERB
ejpam-3363	6	25	[	[	X
ejpam-3363	6	26	2–4	2–4	NUM
ejpam-3363	6	27	,	,	PUNCT
ejpam-3363	6	28	7–9	7–9	NOUN
ejpam-3363	6	29	]	]	X
ejpam-3363	6	30	.	.	PUNCT
ejpam-3363	7	1	the	the	DET
ejpam-3363	7	2	henstockkurzweil	henstockkurzweil	NOUN
ejpam-3363	7	3	integral	integral	ADJ
ejpam-3363	7	4	is	be	AUX
ejpam-3363	7	5	a	a	DET
ejpam-3363	7	6	riemann	riemann	NOUN
ejpam-3363	7	7	-	-	PUNCT
ejpam-3363	7	8	type	type	NOUN
ejpam-3363	7	9	definition	definition	NOUN
ejpam-3363	7	10	of	of	ADP
ejpam-3363	7	11	an	an	DET
ejpam-3363	7	12	integral	integral	ADJ
ejpam-3363	7	13	which	which	PRON
ejpam-3363	7	14	is	be	AUX
ejpam-3363	7	15	more	more	ADV
ejpam-3363	7	16	explicit	explicit	ADJ
ejpam-3363	7	17	and	and	CCONJ
ejpam-3363	7	18	minimizes	minimize	VERB
ejpam-3363	7	19	the	the	DET
ejpam-3363	7	20	technicalities	technicality	NOUN
ejpam-3363	7	21	in	in	ADP
ejpam-3363	7	22	the	the	DET
ejpam-3363	7	23	classical	classical	ADJ
ejpam-3363	7	24	approach	approach	NOUN
ejpam-3363	7	25	of	of	ADP
ejpam-3363	7	26	the	the	DET
ejpam-3363	7	27	lebesgue	lebesgue	NOUN
ejpam-3363	7	28	integral	integral	ADJ
ejpam-3363	7	29	.	.	PUNCT
ejpam-3363	8	1	this	this	DET
ejpam-3363	8	2	approach	approach	NOUN
ejpam-3363	8	3	to	to	ADP
ejpam-3363	8	4	integration	integration	NOUN
ejpam-3363	8	5	is	be	AUX
ejpam-3363	8	6	known	know	VERB
ejpam-3363	8	7	as	as	ADP
ejpam-3363	8	8	the	the	DET
ejpam-3363	8	9	generalized	generalize	VERB
ejpam-3363	8	10	riemann	riemann	PROPN
ejpam-3363	8	11	approach	approach	NOUN
ejpam-3363	8	12	or	or	CCONJ
ejpam-3363	8	13	henstock	henstock	NOUN
ejpam-3363	8	14	approach	approach	NOUN
ejpam-3363	8	15	.	.	PUNCT
ejpam-3363	9	1	in	in	ADP
ejpam-3363	9	2	the	the	DET
ejpam-3363	9	3	classical	classical	ADJ
ejpam-3363	9	4	approach	approach	NOUN
ejpam-3363	9	5	to	to	ADP
ejpam-3363	9	6	stochastic	stochastic	ADJ
ejpam-3363	9	7	integration	integration	NOUN
ejpam-3363	9	8	,	,	PUNCT
ejpam-3363	9	9	the	the	DET
ejpam-3363	9	10	itô	itô	PROPN
ejpam-3363	9	11	integral	integral	ADJ
ejpam-3363	9	12	of	of	ADP
ejpam-3363	9	13	a	a	DET
ejpam-3363	9	14	real	real	ADV
ejpam-3363	9	15	-	-	PUNCT
ejpam-3363	9	16	valued	value	VERB
ejpam-3363	9	17	stochastic	stochastic	ADJ
ejpam-3363	9	18	process	process	NOUN
ejpam-3363	9	19	,	,	PUNCT
ejpam-3363	9	20	which	which	PRON
ejpam-3363	9	21	is	be	AUX
ejpam-3363	9	22	adapted	adapt	VERB
ejpam-3363	9	23	to	to	ADP
ejpam-3363	9	24	a	a	DET
ejpam-3363	9	25	filtration	filtration	NOUN
ejpam-3363	9	26	,	,	PUNCT
ejpam-3363	9	27	is	be	AUX
ejpam-3363	9	28	attained	attain	VERB
ejpam-3363	9	29	from	from	ADP
ejpam-3363	9	30	a	a	DET
ejpam-3363	9	31	limit	limit	NOUN
ejpam-3363	9	32	of	of	ADP
ejpam-3363	9	33	itô	itô	PROPN
ejpam-3363	9	34	integrals	integral	NOUN
ejpam-3363	9	35	of	of	ADP
ejpam-3363	9	36	simple	simple	ADJ
ejpam-3363	9	37	processes	process	NOUN
ejpam-3363	9	38	.	.	PUNCT
ejpam-3363	10	1	to	to	PART
ejpam-3363	10	2	give	give	VERB
ejpam-3363	10	3	a	a	DET
ejpam-3363	10	4	more	more	ADV
ejpam-3363	10	5	explicit	explicit	ADJ
ejpam-3363	10	6	definition	definition	NOUN
ejpam-3363	10	7	and	and	CCONJ
ejpam-3363	10	8	reduce	reduce	VERB
ejpam-3363	10	9	the	the	DET
ejpam-3363	10	10	technicalities	technicality	NOUN
ejpam-3363	10	11	in	in	ADP
ejpam-3363	10	12	the	the	DET
ejpam-3363	10	13	classical	classical	ADJ
ejpam-3363	10	14	way	way	NOUN
ejpam-3363	10	15	of	of	ADP
ejpam-3363	10	16	defining	define	VERB
ejpam-3363	10	17	the	the	DET
ejpam-3363	10	18	itô	itô	PROPN
ejpam-3363	10	19	integral	integral	ADJ
ejpam-3363	10	20	in	in	ADP
ejpam-3363	10	21	the	the	DET
ejpam-3363	10	22	real	real	ADV
ejpam-3363	10	23	-	-	PUNCT
ejpam-3363	10	24	valued	value	VERB
ejpam-3363	10	25	case	case	NOUN
ejpam-3363	10	26	,	,	PUNCT
ejpam-3363	10	27	henstock	henstock	NOUN
ejpam-3363	10	28	approach	approach	NOUN
ejpam-3363	10	29	to	to	ADP
ejpam-3363	10	30	stochastic	stochastic	ADJ
ejpam-3363	10	31	integration	integration	NOUN
ejpam-3363	10	32	had	have	AUX
ejpam-3363	10	33	already	already	ADV
ejpam-3363	10	34	been	be	AUX
ejpam-3363	10	35	studied	study	VERB
ejpam-3363	10	36	in	in	ADP
ejpam-3363	10	37	several	several	ADJ
ejpam-3363	10	38	papers	paper	NOUN
ejpam-3363	10	39	,	,	PUNCT
ejpam-3363	10	40	see	see	VERB
ejpam-3363	10	41	[	[	X
ejpam-3363	10	42	10	10	NUM
ejpam-3363	10	43	,	,	PUNCT
ejpam-3363	10	44	11	11	NUM
ejpam-3363	10	45	,	,	PUNCT
ejpam-3363	10	46	15–17	15–17	NUM
ejpam-3363	10	47	]	]	PUNCT
ejpam-3363	10	48	.	.	PUNCT
ejpam-3363	11	1	∗corresponding	∗corresponde	VERB
ejpam-3363	11	2	author	author	NOUN
ejpam-3363	11	3	.	.	PUNCT
ejpam-3363	12	1	doi	doi	NOUN
ejpam-3363	12	2	:	:	PUNCT
ejpam-3363	12	3	https://doi.org/10.29020/nybg.ejpam.v12i1.3331	https://doi.org/10.29020/nybg.ejpam.v12i1.3331	NUM
ejpam-3363	12	4	email	email	NOUN
ejpam-3363	12	5	addresses	address	NOUN
ejpam-3363	12	6	:	:	PUNCT
ejpam-3363	13	1	jdacagubcob@gmail.com	jdacagubcob@gmail.com	X
ejpam-3363	13	2	(	(	PUNCT
ejpam-3363	13	3	j.d	j.d	PROPN
ejpam-3363	13	4	.	.	PROPN
ejpam-3363	13	5	cagubcob	cagubcob	PROPN
ejpam-3363	13	6	)	)	PUNCT
ejpam-3363	13	7	,	,	PUNCT
ejpam-3363	13	8	mhelmar.labendia@g.msuiit.edu.ph	mhelmar.labendia@g.msuiit.edu.ph	PROPN
ejpam-3363	13	9	(	(	PUNCT
ejpam-3363	13	10	m.	m.	NOUN
ejpam-3363	13	11	labendia	labendia	PROPN
ejpam-3363	13	12	)	)	PUNCT
ejpam-3363	13	13	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3363	14	1	101	101	NUM
ejpam-3363	14	2	c	c	X
ejpam-3363	14	3	©	©	PROPN
ejpam-3363	14	4	2019	2019	NUM
ejpam-3363	14	5	ejpam	ejpam	NOUN
ejpam-3363	14	6	all	all	DET
ejpam-3363	14	7	rights	right	NOUN
ejpam-3363	14	8	reserved	reserve	VERB
ejpam-3363	14	9	.	.	PUNCT
ejpam-3363	15	1	j.d	j.d	PROPN
ejpam-3363	15	2	.	.	PROPN
ejpam-3363	15	3	cagubcob	cagubcob	PROPN
ejpam-3363	15	4	,	,	PUNCT
ejpam-3363	15	5	m.	m.	NOUN
ejpam-3363	15	6	labendia	labendia	PROPN
ejpam-3363	15	7	/	/	SYM
ejpam-3363	15	8	eur	eur	PROPN
ejpam-3363	15	9	.	.	PUNCT
ejpam-3363	16	1	j.	j.	PROPN
ejpam-3363	16	2	pure	pure	PROPN
ejpam-3363	16	3	appl	appl	PROPN
ejpam-3363	16	4	.	.	PROPN
ejpam-3363	16	5	math	math	PROPN
ejpam-3363	16	6	,	,	PUNCT
ejpam-3363	16	7	12	12	NUM
ejpam-3363	16	8	(	(	PUNCT
ejpam-3363	16	9	1	1	NUM
ejpam-3363	16	10	)	)	PUNCT
ejpam-3363	16	11	(	(	PUNCT
ejpam-3363	16	12	2019	2019	NUM
ejpam-3363	16	13	)	)	PUNCT
ejpam-3363	16	14	,	,	PUNCT
ejpam-3363	16	15	101	101	NUM
ejpam-3363	16	16	-	-	SYM
ejpam-3363	16	17	117	117	NUM
ejpam-3363	16	18	102	102	NUM
ejpam-3363	16	19	in	in	ADP
ejpam-3363	16	20	infinite	infinite	ADJ
ejpam-3363	16	21	dimensional	dimensional	ADJ
ejpam-3363	16	22	spaces	space	NOUN
ejpam-3363	16	23	,	,	PUNCT
ejpam-3363	16	24	the	the	DET
ejpam-3363	16	25	itô	itô	PROPN
ejpam-3363	16	26	integral	integral	ADJ
ejpam-3363	16	27	of	of	ADP
ejpam-3363	16	28	an	an	DET
ejpam-3363	16	29	operator	operator	NOUN
ejpam-3363	16	30	-	-	PUNCT
ejpam-3363	16	31	valued	value	VERB
ejpam-3363	16	32	stochastic	stochastic	ADJ
ejpam-3363	16	33	process	process	NOUN
ejpam-3363	16	34	,	,	PUNCT
ejpam-3363	16	35	adapted	adapt	VERB
ejpam-3363	16	36	to	to	ADP
ejpam-3363	16	37	a	a	DET
ejpam-3363	16	38	normal	normal	ADJ
ejpam-3363	16	39	filtration	filtration	NOUN
ejpam-3363	16	40	,	,	PUNCT
ejpam-3363	16	41	is	be	AUX
ejpam-3363	16	42	obtained	obtain	VERB
ejpam-3363	16	43	by	by	ADP
ejpam-3363	16	44	extending	extend	VERB
ejpam-3363	16	45	an	an	DET
ejpam-3363	16	46	isometry	isometry	NOUN
ejpam-3363	16	47	from	from	ADP
ejpam-3363	16	48	the	the	DET
ejpam-3363	16	49	space	space	NOUN
ejpam-3363	16	50	of	of	ADP
ejpam-3363	16	51	elementary	elementary	ADJ
ejpam-3363	16	52	processes	process	NOUN
ejpam-3363	16	53	to	to	ADP
ejpam-3363	16	54	the	the	DET
ejpam-3363	16	55	space	space	NOUN
ejpam-3363	16	56	of	of	ADP
ejpam-3363	16	57	continuous	continuous	ADJ
ejpam-3363	16	58	square	square	ADJ
ejpam-3363	16	59	-	-	PUNCT
ejpam-3363	16	60	integrable	integrable	ADJ
ejpam-3363	16	61	martingales	martingale	NOUN
ejpam-3363	16	62	.	.	PUNCT
ejpam-3363	17	1	in	in	ADP
ejpam-3363	17	2	this	this	DET
ejpam-3363	17	3	case	case	NOUN
ejpam-3363	17	4	,	,	PUNCT
ejpam-3363	17	5	the	the	DET
ejpam-3363	17	6	value	value	NOUN
ejpam-3363	17	7	of	of	ADP
ejpam-3363	17	8	the	the	DET
ejpam-3363	17	9	integrand	integrand	NOUN
ejpam-3363	17	10	is	be	AUX
ejpam-3363	17	11	an	an	DET
ejpam-3363	17	12	operator	operator	NOUN
ejpam-3363	17	13	and	and	CCONJ
ejpam-3363	17	14	the	the	DET
ejpam-3363	17	15	integrator	integrator	NOUN
ejpam-3363	17	16	is	be	AUX
ejpam-3363	17	17	a	a	DET
ejpam-3363	17	18	q	q	ADJ
ejpam-3363	17	19	-	-	PUNCT
ejpam-3363	17	20	wiener	wiener	NOUN
ejpam-3363	17	21	process	process	NOUN
ejpam-3363	17	22	,	,	PUNCT
ejpam-3363	17	23	a	a	DET
ejpam-3363	17	24	hilbert	hilbert	NOUN
ejpam-3363	17	25	space	space	NOUN
ejpam-3363	17	26	-	-	PUNCT
ejpam-3363	17	27	valued	value	VERB
ejpam-3363	17	28	wiener	wiener	NOUN
ejpam-3363	17	29	process	process	NOUN
ejpam-3363	17	30	which	which	PRON
ejpam-3363	17	31	is	be	AUX
ejpam-3363	17	32	dependent	dependent	ADJ
ejpam-3363	17	33	on	on	ADP
ejpam-3363	17	34	a	a	DET
ejpam-3363	17	35	symmetric	symmetric	ADJ
ejpam-3363	17	36	nonnegative	nonnegative	ADJ
ejpam-3363	17	37	definite	definite	ADJ
ejpam-3363	17	38	trace	trace	NOUN
ejpam-3363	17	39	-	-	PUNCT
ejpam-3363	17	40	class	class	NOUN
ejpam-3363	17	41	operator	operator	NOUN
ejpam-3363	17	42	q.	q.	NOUN
ejpam-3363	17	43	in	in	ADP
ejpam-3363	17	44	this	this	DET
ejpam-3363	17	45	paper	paper	NOUN
ejpam-3363	17	46	,	,	PUNCT
ejpam-3363	17	47	we	we	PRON
ejpam-3363	17	48	formulate	formulate	VERB
ejpam-3363	17	49	a	a	DET
ejpam-3363	17	50	version	version	NOUN
ejpam-3363	17	51	of	of	ADP
ejpam-3363	17	52	fundamental	fundamental	ADJ
ejpam-3363	17	53	theorem	theorem	NOUN
ejpam-3363	17	54	for	for	ADP
ejpam-3363	17	55	the	the	DET
ejpam-3363	17	56	itô-mcshane	itô-mcshane	NOUN
ejpam-3363	17	57	integral	integral	ADJ
ejpam-3363	17	58	,	,	PUNCT
ejpam-3363	17	59	a	a	DET
ejpam-3363	17	60	henstock	henstock	NOUN
ejpam-3363	17	61	approach	approach	NOUN
ejpam-3363	17	62	integral	integral	ADJ
ejpam-3363	17	63	,	,	PUNCT
ejpam-3363	17	64	for	for	ADP
ejpam-3363	17	65	the	the	DET
ejpam-3363	17	66	operator	operator	NOUN
ejpam-3363	17	67	-	-	PUNCT
ejpam-3363	17	68	valued	value	VERB
ejpam-3363	17	69	stochastic	stochastic	ADJ
ejpam-3363	17	70	process	process	NOUN
ejpam-3363	17	71	with	with	ADP
ejpam-3363	17	72	respect	respect	NOUN
ejpam-3363	17	73	to	to	ADP
ejpam-3363	17	74	a	a	DET
ejpam-3363	17	75	q	q	ADJ
ejpam-3363	17	76	-	-	PUNCT
ejpam-3363	17	77	wiener	wiener	NOUN
ejpam-3363	17	78	process	process	NOUN
ejpam-3363	17	79	.	.	PUNCT
ejpam-3363	18	1	2	2	X
ejpam-3363	18	2	.	.	X
ejpam-3363	18	3	preliminaries	preliminary	NOUN
ejpam-3363	18	4	throughout	throughout	ADP
ejpam-3363	18	5	this	this	DET
ejpam-3363	18	6	paper	paper	NOUN
ejpam-3363	18	7	,	,	PUNCT
ejpam-3363	18	8	let	let	VERB
ejpam-3363	18	9	(	(	PUNCT
ejpam-3363	18	10	ω	ω	PROPN
ejpam-3363	18	11	,	,	PUNCT
ejpam-3363	18	12	f	f	PROPN
ejpam-3363	18	13	,	,	PUNCT
ejpam-3363	18	14	{	{	PUNCT
ejpam-3363	18	15	ft},p	ft},p	NOUN
ejpam-3363	18	16	)	)	PUNCT
ejpam-3363	18	17	be	be	VERB
ejpam-3363	18	18	a	a	DET
ejpam-3363	18	19	filtered	filter	VERB
ejpam-3363	18	20	probability	probability	NOUN
ejpam-3363	18	21	space	space	NOUN
ejpam-3363	18	22	,	,	PUNCT
ejpam-3363	18	23	b(h	b(h	PROPN
ejpam-3363	18	24	)	)	PUNCT
ejpam-3363	18	25	be	be	VERB
ejpam-3363	18	26	the	the	DET
ejpam-3363	18	27	borel	borel	PROPN
ejpam-3363	18	28	σ	σ	PROPN
ejpam-3363	18	29	-	-	PUNCT
ejpam-3363	18	30	field	field	NOUN
ejpam-3363	18	31	of	of	ADP
ejpam-3363	18	32	a	a	DET
ejpam-3363	18	33	separable	separable	ADJ
ejpam-3363	18	34	banach	banach	NOUN
ejpam-3363	18	35	space	space	NOUN
ejpam-3363	18	36	h	h	NOUN
ejpam-3363	18	37	,	,	PUNCT
ejpam-3363	18	38	and	and	CCONJ
ejpam-3363	18	39	l(h	l(h	PRON
ejpam-3363	18	40	)	)	PUNCT
ejpam-3363	18	41	be	be	VERB
ejpam-3363	18	42	the	the	DET
ejpam-3363	18	43	probability	probability	NOUN
ejpam-3363	18	44	distribution	distribution	NOUN
ejpam-3363	18	45	or	or	CCONJ
ejpam-3363	18	46	the	the	DET
ejpam-3363	18	47	law	law	NOUN
ejpam-3363	18	48	of	of	ADP
ejpam-3363	18	49	a	a	DET
ejpam-3363	18	50	random	random	ADJ
ejpam-3363	18	51	variable	variable	ADJ
ejpam-3363	18	52	h	h	NOUN
ejpam-3363	18	53	:	:	PUNCT
ejpam-3363	18	54	ω→	ω→	PUNCT
ejpam-3363	18	55	h.	h.	PROPN
ejpam-3363	18	56	a	a	DET
ejpam-3363	18	57	stochastic	stochastic	ADJ
ejpam-3363	18	58	process	process	NOUN
ejpam-3363	18	59	f	f	NOUN
ejpam-3363	18	60	:	:	PUNCT
ejpam-3363	19	1	[	[	X
ejpam-3363	19	2	0	0	NUM
ejpam-3363	19	3	,	,	PUNCT
ejpam-3363	19	4	t	t	X
ejpam-3363	19	5	]	]	PUNCT
ejpam-3363	19	6	×	×	PROPN
ejpam-3363	19	7	ω	ω	PROPN
ejpam-3363	19	8	→	→	SYM
ejpam-3363	19	9	h	h	NOUN
ejpam-3363	19	10	,	,	PUNCT
ejpam-3363	19	11	or	or	CCONJ
ejpam-3363	19	12	simply	simply	ADV
ejpam-3363	19	13	a	a	DET
ejpam-3363	19	14	process	process	NOUN
ejpam-3363	19	15	{	{	PUNCT
ejpam-3363	19	16	ft}0≤t≤t	ft}0≤t≤t	NOUN
ejpam-3363	19	17	,	,	PUNCT
ejpam-3363	19	18	is	be	AUX
ejpam-3363	19	19	said	say	VERB
ejpam-3363	19	20	to	to	PART
ejpam-3363	19	21	be	be	AUX
ejpam-3363	19	22	adapted	adapt	VERB
ejpam-3363	19	23	to	to	ADP
ejpam-3363	19	24	a	a	DET
ejpam-3363	19	25	filtration	filtration	NOUN
ejpam-3363	19	26	{	{	PUNCT
ejpam-3363	19	27	ft	ft	NOUN
ejpam-3363	19	28	}	}	PUNCT
ejpam-3363	19	29	if	if	SCONJ
ejpam-3363	19	30	ft	ft	NOUN
ejpam-3363	19	31	is	be	AUX
ejpam-3363	19	32	ft	ft	NOUN
ejpam-3363	19	33	-	-	PUNCT
ejpam-3363	19	34	measurable	measurable	NOUN
ejpam-3363	19	35	for	for	ADP
ejpam-3363	19	36	all	all	DET
ejpam-3363	19	37	t	t	NOUN
ejpam-3363	19	38	∈	∈	PROPN
ejpam-3363	20	1	[	[	X
ejpam-3363	20	2	0	0	NUM
ejpam-3363	20	3	,	,	PUNCT
ejpam-3363	20	4	t	t	X
ejpam-3363	20	5	]	]	PUNCT
ejpam-3363	20	6	.	.	PUNCT
ejpam-3363	21	1	when	when	SCONJ
ejpam-3363	21	2	no	no	DET
ejpam-3363	21	3	confusion	confusion	NOUN
ejpam-3363	21	4	arises	arise	VERB
ejpam-3363	21	5	,	,	PUNCT
ejpam-3363	21	6	we	we	PRON
ejpam-3363	21	7	may	may	AUX
ejpam-3363	21	8	refer	refer	VERB
ejpam-3363	21	9	to	to	ADP
ejpam-3363	21	10	a	a	DET
ejpam-3363	21	11	process	process	NOUN
ejpam-3363	21	12	adapted	adapt	VERB
ejpam-3363	21	13	to	to	ADP
ejpam-3363	21	14	{	{	PUNCT
ejpam-3363	21	15	ft	ft	NOUN
ejpam-3363	21	16	}	}	PUNCT
ejpam-3363	21	17	as	as	ADP
ejpam-3363	21	18	simply	simply	ADV
ejpam-3363	21	19	an	an	DET
ejpam-3363	21	20	adapted	adapt	VERB
ejpam-3363	21	21	process	process	NOUN
ejpam-3363	21	22	.	.	PUNCT
ejpam-3363	22	1	let	let	VERB
ejpam-3363	22	2	u	u	PRON
ejpam-3363	22	3	and	and	CCONJ
ejpam-3363	22	4	v	v	NOUN
ejpam-3363	22	5	be	be	AUX
ejpam-3363	22	6	separable	separable	ADJ
ejpam-3363	22	7	hilbert	hilbert	PROPN
ejpam-3363	22	8	spaces	space	NOUN
ejpam-3363	22	9	.	.	PUNCT
ejpam-3363	23	1	denote	denote	VERB
ejpam-3363	23	2	by	by	ADP
ejpam-3363	23	3	l(u	l(u	PROPN
ejpam-3363	23	4	,	,	PUNCT
ejpam-3363	23	5	v	v	NOUN
ejpam-3363	23	6	)	)	PUNCT
ejpam-3363	23	7	the	the	DET
ejpam-3363	23	8	space	space	NOUN
ejpam-3363	23	9	of	of	ADP
ejpam-3363	23	10	all	all	DET
ejpam-3363	23	11	bounded	bound	VERB
ejpam-3363	23	12	linear	linear	PROPN
ejpam-3363	23	13	operators	operator	NOUN
ejpam-3363	23	14	from	from	ADP
ejpam-3363	23	15	u	u	PRON
ejpam-3363	23	16	to	to	ADP
ejpam-3363	23	17	v	v	NUM
ejpam-3363	23	18	,	,	PUNCT
ejpam-3363	23	19	l(u	l(u	PROPN
ejpam-3363	23	20	)	)	PUNCT
ejpam-3363	23	21	:	:	PUNCT
ejpam-3363	24	1	=	=	SYM
ejpam-3363	24	2	l(u	l(u	PROPN
ejpam-3363	24	3	,	,	PUNCT
ejpam-3363	24	4	u	u	NOUN
ejpam-3363	24	5	)	)	PUNCT
ejpam-3363	24	6	,	,	PUNCT
ejpam-3363	24	7	qu	qu	PROPN
ejpam-3363	24	8	:	:	PUNCT
ejpam-3363	24	9	=	=	SYM
ejpam-3363	24	10	q(u	q(u	X
ejpam-3363	24	11	)	)	PUNCT
ejpam-3363	24	12	for	for	ADP
ejpam-3363	24	13	q	q	PROPN
ejpam-3363	24	14	∈	∈	PROPN
ejpam-3363	24	15	l(u	l(u	PROPN
ejpam-3363	24	16	,	,	PUNCT
ejpam-3363	24	17	v	v	NOUN
ejpam-3363	24	18	)	)	PUNCT
ejpam-3363	24	19	,	,	PUNCT
ejpam-3363	24	20	and	and	CCONJ
ejpam-3363	24	21	l2(ω	l2(ω	PROPN
ejpam-3363	24	22	,	,	PUNCT
ejpam-3363	24	23	v	v	NOUN
ejpam-3363	24	24	)	)	PUNCT
ejpam-3363	24	25	the	the	DET
ejpam-3363	24	26	space	space	NOUN
ejpam-3363	24	27	of	of	ADP
ejpam-3363	24	28	all	all	DET
ejpam-3363	24	29	square	square	ADJ
ejpam-3363	24	30	-	-	PUNCT
ejpam-3363	24	31	integrable	integrable	ADJ
ejpam-3363	24	32	random	random	ADJ
ejpam-3363	24	33	variables	variable	NOUN
ejpam-3363	24	34	from	from	ADP
ejpam-3363	24	35	ω	ω	NUM
ejpam-3363	24	36	to	to	ADP
ejpam-3363	24	37	v	v	NOUN
ejpam-3363	24	38	.	.	PUNCT
ejpam-3363	25	1	an	an	DET
ejpam-3363	25	2	operator	operator	NOUN
ejpam-3363	25	3	q	q	PROPN
ejpam-3363	25	4	∈	∈	PROPN
ejpam-3363	25	5	l(u	l(u	PROPN
ejpam-3363	25	6	)	)	PUNCT
ejpam-3363	25	7	is	be	AUX
ejpam-3363	25	8	said	say	VERB
ejpam-3363	25	9	to	to	PART
ejpam-3363	25	10	be	be	AUX
ejpam-3363	25	11	self	self	NOUN
ejpam-3363	25	12	-	-	PUNCT
ejpam-3363	25	13	adjoint	adjoint	NOUN
ejpam-3363	25	14	or	or	CCONJ
ejpam-3363	25	15	symmetric	symmetric	ADJ
ejpam-3363	25	16	if	if	SCONJ
ejpam-3363	25	17	for	for	ADP
ejpam-3363	25	18	all	all	DET
ejpam-3363	25	19	u	u	NOUN
ejpam-3363	25	20	,	,	PUNCT
ejpam-3363	25	21	u′	u′	PROPN
ejpam-3363	25	22	∈	∈	PROPN
ejpam-3363	25	23	u	u	PROPN
ejpam-3363	25	24	,	,	PUNCT
ejpam-3363	25	25	〈	〈	PROPN
ejpam-3363	25	26	qu	qu	PROPN
ejpam-3363	25	27	,	,	PUNCT
ejpam-3363	25	28	u′〉u	u′〉u	PROPN
ejpam-3363	25	29	=	=	SYM
ejpam-3363	25	30	〈	〈	PROPN
ejpam-3363	25	31	u	u	NOUN
ejpam-3363	25	32	,	,	PUNCT
ejpam-3363	25	33	qu′〉u	qu′〉u	PROPN
ejpam-3363	25	34	and	and	CCONJ
ejpam-3363	25	35	is	be	AUX
ejpam-3363	25	36	said	say	VERB
ejpam-3363	25	37	to	to	PART
ejpam-3363	25	38	be	be	AUX
ejpam-3363	25	39	nonnegative	nonnegative	ADJ
ejpam-3363	25	40	definite	definite	ADJ
ejpam-3363	25	41	if	if	SCONJ
ejpam-3363	25	42	for	for	ADP
ejpam-3363	25	43	every	every	DET
ejpam-3363	25	44	u	u	PROPN
ejpam-3363	25	45	∈	∈	PROPN
ejpam-3363	25	46	u	u	NOUN
ejpam-3363	25	47	,	,	PUNCT
ejpam-3363	25	48	〈	〈	PROPN
ejpam-3363	25	49	qu	qu	PROPN
ejpam-3363	25	50	,	,	PUNCT
ejpam-3363	25	51	u〉u	u〉u	NOUN
ejpam-3363	25	52	≥	≥	NUM
ejpam-3363	25	53	0	0	NUM
ejpam-3363	25	54	.	.	PUNCT
ejpam-3363	26	1	using	use	VERB
ejpam-3363	26	2	the	the	DET
ejpam-3363	26	3	square	square	ADJ
ejpam-3363	26	4	-	-	PUNCT
ejpam-3363	26	5	root	root	NOUN
ejpam-3363	26	6	lemma	lemma	PROPN
ejpam-3363	27	1	[	[	X
ejpam-3363	27	2	14	14	NUM
ejpam-3363	27	3	,	,	PUNCT
ejpam-3363	27	4	p.196	p.196	VERB
ejpam-3363	27	5	]	]	X
ejpam-3363	27	6	,	,	PUNCT
ejpam-3363	27	7	if	if	SCONJ
ejpam-3363	27	8	q	q	PROPN
ejpam-3363	27	9	∈	∈	PROPN
ejpam-3363	27	10	l(u	l(u	PROPN
ejpam-3363	27	11	)	)	PUNCT
ejpam-3363	27	12	is	be	AUX
ejpam-3363	27	13	nonnegative	nonnegative	ADJ
ejpam-3363	27	14	definite	definite	ADJ
ejpam-3363	27	15	,	,	PUNCT
ejpam-3363	27	16	then	then	ADV
ejpam-3363	27	17	there	there	PRON
ejpam-3363	27	18	exists	exist	VERB
ejpam-3363	27	19	a	a	DET
ejpam-3363	27	20	unique	unique	ADJ
ejpam-3363	27	21	operator	operator	NOUN
ejpam-3363	27	22	q	q	NOUN
ejpam-3363	27	23	1	1	NUM
ejpam-3363	27	24	2	2	NUM
ejpam-3363	27	25	∈	∈	PROPN
ejpam-3363	27	26	l(u	l(u	PROPN
ejpam-3363	27	27	)	)	PUNCT
ejpam-3363	27	28	such	such	ADJ
ejpam-3363	27	29	that	that	PRON
ejpam-3363	27	30	q	q	NOUN
ejpam-3363	27	31	1	1	NUM
ejpam-3363	27	32	2	2	NUM
ejpam-3363	27	33	is	be	AUX
ejpam-3363	27	34	nonnegative	nonnegative	ADJ
ejpam-3363	27	35	definite	definite	ADJ
ejpam-3363	27	36	and	and	CCONJ
ejpam-3363	27	37	q	q	NOUN
ejpam-3363	27	38	1	1	NUM
ejpam-3363	27	39	2	2	NUM
ejpam-3363	27	40	◦	◦	NOUN
ejpam-3363	27	41	q	q	NOUN
ejpam-3363	27	42	1	1	NUM
ejpam-3363	27	43	2	2	NUM
ejpam-3363	27	44	=	=	SYM
ejpam-3363	27	45	q.	q.	NOUN
ejpam-3363	27	46	let	let	VERB
ejpam-3363	27	47	{	{	PUNCT
ejpam-3363	27	48	ej}∞j=1	ej}∞j=1	X
ejpam-3363	27	49	,	,	PUNCT
ejpam-3363	27	50	or	or	CCONJ
ejpam-3363	27	51	simply	simply	ADV
ejpam-3363	27	52	{	{	PUNCT
ejpam-3363	27	53	ej	ej	NOUN
ejpam-3363	27	54	}	}	PUNCT
ejpam-3363	27	55	,	,	PUNCT
ejpam-3363	27	56	be	be	AUX
ejpam-3363	27	57	an	an	DET
ejpam-3363	27	58	orthonormal	orthonormal	ADJ
ejpam-3363	27	59	basis	basis	NOUN
ejpam-3363	27	60	(	(	PUNCT
ejpam-3363	27	61	abbrev	abbrev	NOUN
ejpam-3363	27	62	.	.	PUNCT
ejpam-3363	28	1	as	as	ADP
ejpam-3363	28	2	onb	onb	ADJ
ejpam-3363	28	3	)	)	PUNCT
ejpam-3363	28	4	in	in	ADP
ejpam-3363	28	5	u	u	NOUN
ejpam-3363	28	6	.	.	PUNCT
ejpam-3363	29	1	if	if	SCONJ
ejpam-3363	29	2	q	q	PROPN
ejpam-3363	29	3	∈	∈	PROPN
ejpam-3363	29	4	l(u	l(u	PROPN
ejpam-3363	29	5	)	)	PUNCT
ejpam-3363	29	6	is	be	AUX
ejpam-3363	29	7	nonnegative	nonnegative	ADJ
ejpam-3363	29	8	definite	definite	ADJ
ejpam-3363	29	9	,	,	PUNCT
ejpam-3363	29	10	then	then	ADV
ejpam-3363	29	11	the	the	DET
ejpam-3363	29	12	trace	trace	NOUN
ejpam-3363	29	13	of	of	ADP
ejpam-3363	29	14	q	q	NOUN
ejpam-3363	29	15	is	be	AUX
ejpam-3363	29	16	defined	define	VERB
ejpam-3363	29	17	by	by	ADP
ejpam-3363	29	18	tr	tr	VERB
ejpam-3363	29	19	q	q	NOUN
ejpam-3363	29	20	=	=	PUNCT
ejpam-3363	29	21	∑∞	∑∞	NOUN
ejpam-3363	29	22	j=1	j=1	PROPN
ejpam-3363	29	23	〈	〈	PROPN
ejpam-3363	29	24	qej	qej	NOUN
ejpam-3363	29	25	,	,	PUNCT
ejpam-3363	29	26	ej〉u	ej〉u	NOUN
ejpam-3363	29	27	.	.	PUNCT
ejpam-3363	30	1	it	it	PRON
ejpam-3363	30	2	is	be	AUX
ejpam-3363	30	3	shown	show	VERB
ejpam-3363	30	4	in	in	ADP
ejpam-3363	30	5	[	[	X
ejpam-3363	30	6	14	14	NUM
ejpam-3363	30	7	,	,	PUNCT
ejpam-3363	30	8	p.206	p.206	NOUN
ejpam-3363	30	9	]	]	PUNCT
ejpam-3363	30	10	that	that	PRON
ejpam-3363	30	11	tr	tr	VERB
ejpam-3363	30	12	q	q	PROPN
ejpam-3363	30	13	is	be	AUX
ejpam-3363	30	14	well	well	ADV
ejpam-3363	30	15	-	-	PUNCT
ejpam-3363	30	16	defined	define	VERB
ejpam-3363	30	17	and	and	CCONJ
ejpam-3363	30	18	may	may	AUX
ejpam-3363	30	19	be	be	AUX
ejpam-3363	30	20	defined	define	VERB
ejpam-3363	30	21	in	in	ADP
ejpam-3363	30	22	terms	term	NOUN
ejpam-3363	30	23	of	of	ADP
ejpam-3363	30	24	an	an	DET
ejpam-3363	30	25	arbitrary	arbitrary	ADJ
ejpam-3363	30	26	onb	onb	ADJ
ejpam-3363	30	27	.	.	PUNCT
ejpam-3363	31	1	an	an	DET
ejpam-3363	31	2	operator	operator	NOUN
ejpam-3363	31	3	q	q	NOUN
ejpam-3363	31	4	:	:	PUNCT
ejpam-3363	31	5	u	u	PROPN
ejpam-3363	31	6	→	→	SYM
ejpam-3363	31	7	u	u	NOUN
ejpam-3363	31	8	is	be	AUX
ejpam-3363	31	9	said	say	VERB
ejpam-3363	31	10	to	to	PART
ejpam-3363	31	11	be	be	AUX
ejpam-3363	31	12	trace	trace	NOUN
ejpam-3363	31	13	-	-	PUNCT
ejpam-3363	31	14	class	class	NOUN
ejpam-3363	31	15	if	if	SCONJ
ejpam-3363	31	16	tr	tr	VERB
ejpam-3363	31	17	[	[	X
ejpam-3363	31	18	q	q	X
ejpam-3363	31	19	]	]	X
ejpam-3363	31	20	:	:	PUNCT
ejpam-3363	31	21	=	=	PUNCT
ejpam-3363	31	22	tr	tr	VERB
ejpam-3363	31	23	(	(	PUNCT
ejpam-3363	31	24	qq∗	qq∗	ADJ
ejpam-3363	31	25	)	)	PUNCT
ejpam-3363	31	26	1	1	NUM
ejpam-3363	31	27	2	2	NUM
ejpam-3363	31	28	<	<	X
ejpam-3363	31	29	∞.	∞.	PROPN
ejpam-3363	31	30	denote	denote	VERB
ejpam-3363	31	31	by	by	ADP
ejpam-3363	31	32	l1(u	l1(u	NOUN
ejpam-3363	31	33	)	)	PUNCT
ejpam-3363	31	34	the	the	DET
ejpam-3363	31	35	space	space	NOUN
ejpam-3363	31	36	of	of	ADP
ejpam-3363	31	37	all	all	DET
ejpam-3363	31	38	trace	trace	NOUN
ejpam-3363	31	39	-	-	PUNCT
ejpam-3363	31	40	class	class	NOUN
ejpam-3363	31	41	operators	operator	NOUN
ejpam-3363	31	42	on	on	ADP
ejpam-3363	31	43	u	u	PROPN
ejpam-3363	31	44	,	,	PUNCT
ejpam-3363	31	45	which	which	PRON
ejpam-3363	31	46	is	be	AUX
ejpam-3363	31	47	known	know	VERB
ejpam-3363	31	48	[	[	X
ejpam-3363	31	49	14	14	NUM
ejpam-3363	31	50	,	,	PUNCT
ejpam-3363	31	51	p.209	p.209	NOUN
ejpam-3363	31	52	]	]	PUNCT
ejpam-3363	31	53	to	to	PART
ejpam-3363	31	54	be	be	AUX
ejpam-3363	31	55	a	a	DET
ejpam-3363	31	56	banach	banach	NOUN
ejpam-3363	31	57	space	space	NOUN
ejpam-3363	31	58	with	with	ADP
ejpam-3363	31	59	norm	norm	NOUN
ejpam-3363	31	60	‖q‖1	‖q‖1	NOUN
ejpam-3363	31	61	=	=	PUNCT
ejpam-3363	31	62	tr	tr	PUNCT
ejpam-3363	31	63	[	[	X
ejpam-3363	31	64	q	q	X
ejpam-3363	31	65	]	]	X
ejpam-3363	31	66	.	.	PUNCT
ejpam-3363	32	1	if	if	SCONJ
ejpam-3363	32	2	q	q	PROPN
ejpam-3363	32	3	∈	∈	PROPN
ejpam-3363	32	4	l(u	l(u	PROPN
ejpam-3363	32	5	)	)	PUNCT
ejpam-3363	32	6	is	be	AUX
ejpam-3363	32	7	a	a	DET
ejpam-3363	32	8	symmetric	symmetric	ADJ
ejpam-3363	32	9	nonnegative	nonnegative	ADJ
ejpam-3363	32	10	definite	definite	ADJ
ejpam-3363	32	11	trace	trace	NOUN
ejpam-3363	32	12	-	-	PUNCT
ejpam-3363	32	13	class	class	NOUN
ejpam-3363	32	14	operator	operator	NOUN
ejpam-3363	32	15	,	,	PUNCT
ejpam-3363	32	16	then	then	ADV
ejpam-3363	32	17	there	there	PRON
ejpam-3363	32	18	exists	exist	VERB
ejpam-3363	32	19	an	an	DET
ejpam-3363	32	20	onb	onb	ADJ
ejpam-3363	32	21	{	{	PUNCT
ejpam-3363	32	22	ej	ej	PROPN
ejpam-3363	32	23	}	}	PUNCT
ejpam-3363	32	24	⊂	⊂	PROPN
ejpam-3363	32	25	u	u	NOUN
ejpam-3363	32	26	and	and	CCONJ
ejpam-3363	32	27	a	a	DET
ejpam-3363	32	28	sequence	sequence	NOUN
ejpam-3363	32	29	of	of	ADP
ejpam-3363	32	30	nonnegative	nonnegative	ADJ
ejpam-3363	32	31	real	real	ADJ
ejpam-3363	32	32	numbers	number	NOUN
ejpam-3363	32	33	{	{	PUNCT
ejpam-3363	32	34	λj	λj	X
ejpam-3363	32	35	}	}	PUNCT
ejpam-3363	32	36	such	such	ADJ
ejpam-3363	32	37	that	that	DET
ejpam-3363	32	38	qej	qej	NOUN
ejpam-3363	32	39	=	=	PUNCT
ejpam-3363	32	40	λjej	λjej	NOUN
ejpam-3363	32	41	for	for	ADP
ejpam-3363	32	42	all	all	DET
ejpam-3363	32	43	j	j	PROPN
ejpam-3363	32	44	∈	∈	PROPN
ejpam-3363	32	45	n	n	CCONJ
ejpam-3363	32	46	,	,	PUNCT
ejpam-3363	32	47	{	{	PUNCT
ejpam-3363	32	48	λj	λj	PROPN
ejpam-3363	32	49	}	}	PUNCT
ejpam-3363	32	50	∈	∈	PROPN
ejpam-3363	32	51	`	`	PUNCT
ejpam-3363	32	52	1	1	NUM
ejpam-3363	32	53	,	,	PUNCT
ejpam-3363	32	54	and	and	CCONJ
ejpam-3363	32	55	λj	λj	X
ejpam-3363	32	56	→	→	SYM
ejpam-3363	32	57	0	0	PUNCT
ejpam-3363	32	58	as	as	ADP
ejpam-3363	32	59	j	j	PROPN
ejpam-3363	32	60	→	→	SYM
ejpam-3363	32	61	∞	∞	PROPN
ejpam-3363	33	1	[	[	X
ejpam-3363	33	2	14	14	NUM
ejpam-3363	33	3	,	,	PUNCT
ejpam-3363	33	4	p.203	p.203	X
ejpam-3363	33	5	]	]	PUNCT
ejpam-3363	33	6	.	.	PUNCT
ejpam-3363	34	1	we	we	PRON
ejpam-3363	34	2	shall	shall	AUX
ejpam-3363	34	3	call	call	VERB
ejpam-3363	34	4	the	the	DET
ejpam-3363	34	5	sequence	sequence	NOUN
ejpam-3363	34	6	of	of	ADP
ejpam-3363	34	7	pairs	pair	NOUN
ejpam-3363	34	8	{	{	PUNCT
ejpam-3363	34	9	λj	λj	NOUN
ejpam-3363	34	10	,	,	PUNCT
ejpam-3363	34	11	ej	ej	PROPN
ejpam-3363	34	12	}	}	PUNCT
ejpam-3363	34	13	an	an	DET
ejpam-3363	34	14	eigensequence	eigensequence	NOUN
ejpam-3363	34	15	defined	define	VERB
ejpam-3363	34	16	by	by	ADP
ejpam-3363	34	17	q.	q.	PROPN
ejpam-3363	34	18	let	let	VERB
ejpam-3363	34	19	q	q	NOUN
ejpam-3363	34	20	:	:	PUNCT
ejpam-3363	34	21	u	u	X
ejpam-3363	34	22	→	→	SYM
ejpam-3363	34	23	u	u	X
ejpam-3363	34	24	be	be	VERB
ejpam-3363	34	25	a	a	DET
ejpam-3363	34	26	symmetric	symmetric	ADJ
ejpam-3363	34	27	nonnegative	nonnegative	ADJ
ejpam-3363	34	28	definite	definite	ADJ
ejpam-3363	34	29	trace	trace	NOUN
ejpam-3363	34	30	-	-	PUNCT
ejpam-3363	34	31	class	class	NOUN
ejpam-3363	34	32	operator	operator	NOUN
ejpam-3363	34	33	.	.	PUNCT
ejpam-3363	35	1	let	let	VERB
ejpam-3363	35	2	{	{	PUNCT
ejpam-3363	35	3	λj	λj	NOUN
ejpam-3363	35	4	,	,	PUNCT
ejpam-3363	35	5	ej	ej	AUX
ejpam-3363	35	6	}	}	PUNCT
ejpam-3363	35	7	be	be	AUX
ejpam-3363	35	8	an	an	DET
ejpam-3363	35	9	eigensequence	eigensequence	NOUN
ejpam-3363	35	10	defined	define	VERB
ejpam-3363	35	11	by	by	ADP
ejpam-3363	35	12	q.	q.	PROPN
ejpam-3363	35	13	then	then	ADV
ejpam-3363	35	14	the	the	DET
ejpam-3363	35	15	subspace	subspace	PROPN
ejpam-3363	35	16	uq	uq	NOUN
ejpam-3363	35	17	:	:	PUNCT
ejpam-3363	35	18	=	=	SYM
ejpam-3363	35	19	q	q	PROPN
ejpam-3363	35	20	1	1	NUM
ejpam-3363	35	21	2u	2u	NOUN
ejpam-3363	35	22	of	of	ADP
ejpam-3363	35	23	u	u	PRON
ejpam-3363	35	24	equipped	equip	VERB
ejpam-3363	35	25	with	with	ADP
ejpam-3363	35	26	the	the	DET
ejpam-3363	35	27	inner	inner	ADJ
ejpam-3363	35	28	product	product	NOUN
ejpam-3363	35	29	〈	〈	PROPN
ejpam-3363	35	30	u	u	NOUN
ejpam-3363	35	31	,	,	PUNCT
ejpam-3363	35	32	v〉uq	v〉uq	NOUN
ejpam-3363	35	33	=	=	SYM
ejpam-3363	35	34	〈	〈	PROPN
ejpam-3363	35	35	q−1/2u	q−1/2u	NOUN
ejpam-3363	35	36	,	,	PUNCT
ejpam-3363	35	37	q−1/2v	q−1/2v	NOUN
ejpam-3363	35	38	〉	〉	NOUN
ejpam-3363	35	39	u	u	NOUN
ejpam-3363	35	40	,	,	PUNCT
ejpam-3363	35	41	where	where	SCONJ
ejpam-3363	35	42	q1/2	q1/2	PROPN
ejpam-3363	35	43	is	be	AUX
ejpam-3363	35	44	being	be	AUX
ejpam-3363	35	45	restricted	restrict	VERB
ejpam-3363	35	46	to	to	ADP
ejpam-3363	35	47	[	[	X
ejpam-3363	35	48	kerq1/2]⊥	kerq1/2]⊥	PROPN
ejpam-3363	35	49	is	be	AUX
ejpam-3363	35	50	a	a	DET
ejpam-3363	35	51	separable	separable	ADJ
ejpam-3363	35	52	hilbert	hilbert	NOUN
ejpam-3363	35	53	space	space	NOUN
ejpam-3363	35	54	with	with	ADP
ejpam-3363	35	55	{	{	PUNCT
ejpam-3363	35	56	√	√	PROPN
ejpam-3363	35	57	λjej	λjej	NOUN
ejpam-3363	35	58	}	}	PUNCT
ejpam-3363	35	59	as	as	ADP
ejpam-3363	35	60	its	its	PRON
ejpam-3363	35	61	onb	onb	ADJ
ejpam-3363	35	62	,	,	PUNCT
ejpam-3363	35	63	see	see	VERB
ejpam-3363	35	64	[	[	X
ejpam-3363	35	65	13	13	NUM
ejpam-3363	35	66	,	,	PUNCT
ejpam-3363	35	67	p.90	p.90	PROPN
ejpam-3363	35	68	]	]	PUNCT
ejpam-3363	35	69	,	,	PUNCT
ejpam-3363	36	1	[	[	X
ejpam-3363	36	2	1	1	NUM
ejpam-3363	36	3	,	,	PUNCT
ejpam-3363	36	4	p.23	p.23	AUX
ejpam-3363	36	5	]	]	PUNCT
ejpam-3363	36	6	.	.	PUNCT
ejpam-3363	37	1	let	let	AUX
ejpam-3363	37	2	{	{	PUNCT
ejpam-3363	37	3	fj	fj	PART
ejpam-3363	37	4	}	}	PUNCT
ejpam-3363	37	5	be	be	AUX
ejpam-3363	37	6	an	an	DET
ejpam-3363	37	7	onb	onb	ADJ
ejpam-3363	37	8	in	in	ADP
ejpam-3363	37	9	uq	uq	NOUN
ejpam-3363	37	10	.	.	PUNCT
ejpam-3363	38	1	an	an	DET
ejpam-3363	38	2	operator	operator	NOUN
ejpam-3363	38	3	s	s	PART
ejpam-3363	38	4	∈	∈	PROPN
ejpam-3363	38	5	l(uq	l(uq	PROPN
ejpam-3363	38	6	,	,	PUNCT
ejpam-3363	38	7	v	v	NOUN
ejpam-3363	38	8	)	)	PUNCT
ejpam-3363	38	9	is	be	AUX
ejpam-3363	38	10	said	say	VERB
ejpam-3363	38	11	to	to	PART
ejpam-3363	38	12	be	be	AUX
ejpam-3363	38	13	hilbert	hilbert	NOUN
ejpam-3363	38	14	-	-	PUNCT
ejpam-3363	38	15	schmidt	schmidt	NOUN
ejpam-3363	38	16	if	if	SCONJ
ejpam-3363	38	17	∑∞	∑∞	VERB
ejpam-3363	38	18	j=1	j=1	X
ejpam-3363	38	19	‖sfj‖	‖sfj‖	PUNCT
ejpam-3363	38	20	2	2	NUM
ejpam-3363	38	21	v	v	NOUN
ejpam-3363	38	22	=	=	PUNCT
ejpam-3363	38	23	∑∞	∑∞	NOUN
ejpam-3363	38	24	j=1	j=1	PROPN
ejpam-3363	38	25	〈	〈	PROPN
ejpam-3363	38	26	sfj	sfj	NOUN
ejpam-3363	38	27	,	,	PUNCT
ejpam-3363	38	28	sfj〉v	sfj〉v	PROPN
ejpam-3363	38	29	<	<	X
ejpam-3363	38	30	∞.	∞.	PROPN
ejpam-3363	38	31	denote	denote	VERB
ejpam-3363	38	32	by	by	ADP
ejpam-3363	38	33	l2(uq	l2(uq	PROPN
ejpam-3363	38	34	,	,	PUNCT
ejpam-3363	38	35	v	v	NOUN
ejpam-3363	38	36	)	)	PUNCT
ejpam-3363	38	37	the	the	DET
ejpam-3363	38	38	space	space	NOUN
ejpam-3363	38	39	of	of	ADP
ejpam-3363	38	40	all	all	DET
ejpam-3363	38	41	hilbertschmidt	hilbertschmidt	ADJ
ejpam-3363	38	42	operators	operator	NOUN
ejpam-3363	38	43	from	from	ADP
ejpam-3363	38	44	uq	uq	NOUN
ejpam-3363	38	45	to	to	ADP
ejpam-3363	38	46	v	v	NOUN
ejpam-3363	38	47	,	,	PUNCT
ejpam-3363	38	48	which	which	PRON
ejpam-3363	38	49	is	be	AUX
ejpam-3363	38	50	known	know	VERB
ejpam-3363	38	51	[	[	X
ejpam-3363	38	52	12	12	NUM
ejpam-3363	38	53	,	,	PUNCT
ejpam-3363	38	54	p.112	p.112	NOUN
ejpam-3363	38	55	]	]	PUNCT
ejpam-3363	38	56	to	to	PART
ejpam-3363	38	57	be	be	AUX
ejpam-3363	38	58	a	a	DET
ejpam-3363	38	59	separable	separable	ADJ
ejpam-3363	38	60	hilbert	hilbert	NOUN
ejpam-3363	38	61	space	space	NOUN
ejpam-3363	38	62	with	with	ADP
ejpam-3363	38	63	norm	norm	NOUN
ejpam-3363	38	64	‖s‖l2(uq	‖s‖l2(uq	NOUN
ejpam-3363	38	65	,	,	PUNCT
ejpam-3363	38	66	v	v	NOUN
ejpam-3363	38	67	)	)	PUNCT
ejpam-3363	38	68	=	=	SYM
ejpam-3363	38	69	√∑∞	√∑∞	VERB
ejpam-3363	38	70	j=1	j=1	NOUN
ejpam-3363	38	71	‖sfj‖	‖sfj‖	PUNCT
ejpam-3363	38	72	2	2	NUM
ejpam-3363	38	73	v	v	NOUN
ejpam-3363	38	74	.	.	PUNCT
ejpam-3363	39	1	the	the	DET
ejpam-3363	39	2	hilbert	hilbert	PROPN
ejpam-3363	39	3	-	-	PUNCT
ejpam-3363	39	4	schmidt	schmidt	NOUN
ejpam-3363	39	5	operator	operator	NOUN
ejpam-3363	39	6	s	s	PART
ejpam-3363	39	7	∈	∈	PROPN
ejpam-3363	39	8	l2(uq	l2(uq	PROPN
ejpam-3363	39	9	,	,	PUNCT
ejpam-3363	39	10	v	v	NOUN
ejpam-3363	39	11	)	)	PUNCT
ejpam-3363	39	12	j.d	j.d	PROPN
ejpam-3363	39	13	.	.	PROPN
ejpam-3363	39	14	cagubcob	cagubcob	PROPN
ejpam-3363	39	15	,	,	PUNCT
ejpam-3363	39	16	m.	m.	NOUN
ejpam-3363	39	17	labendia	labendia	PROPN
ejpam-3363	39	18	/	/	SYM
ejpam-3363	39	19	eur	eur	PROPN
ejpam-3363	39	20	.	.	PUNCT
ejpam-3363	40	1	j.	j.	PROPN
ejpam-3363	40	2	pure	pure	PROPN
ejpam-3363	40	3	appl	appl	PROPN
ejpam-3363	40	4	.	.	PROPN
ejpam-3363	40	5	math	math	PROPN
ejpam-3363	40	6	,	,	PUNCT
ejpam-3363	40	7	12	12	NUM
ejpam-3363	40	8	(	(	PUNCT
ejpam-3363	40	9	1	1	NUM
ejpam-3363	40	10	)	)	PUNCT
ejpam-3363	40	11	(	(	PUNCT
ejpam-3363	40	12	2019	2019	NUM
ejpam-3363	40	13	)	)	PUNCT
ejpam-3363	40	14	,	,	PUNCT
ejpam-3363	40	15	101	101	NUM
ejpam-3363	40	16	-	-	SYM
ejpam-3363	40	17	117	117	NUM
ejpam-3363	40	18	103	103	NUM
ejpam-3363	40	19	and	and	CCONJ
ejpam-3363	40	20	the	the	DET
ejpam-3363	40	21	norm	norm	NOUN
ejpam-3363	40	22	‖s‖l2(uq	‖s‖l2(uq	NOUN
ejpam-3363	40	23	,	,	PUNCT
ejpam-3363	40	24	v	v	NOUN
ejpam-3363	40	25	)	)	PUNCT
ejpam-3363	40	26	may	may	AUX
ejpam-3363	40	27	be	be	AUX
ejpam-3363	40	28	defined	define	VERB
ejpam-3363	40	29	in	in	ADP
ejpam-3363	40	30	terms	term	NOUN
ejpam-3363	40	31	of	of	ADP
ejpam-3363	40	32	an	an	DET
ejpam-3363	40	33	arbitrary	arbitrary	ADJ
ejpam-3363	40	34	onb	onb	ADJ
ejpam-3363	40	35	,	,	PUNCT
ejpam-3363	40	36	see	see	VERB
ejpam-3363	40	37	[	[	X
ejpam-3363	40	38	13	13	NUM
ejpam-3363	40	39	,	,	PUNCT
ejpam-3363	40	40	p.418	p.418	NOUN
ejpam-3363	40	41	]	]	X
ejpam-3363	40	42	,	,	PUNCT
ejpam-3363	41	1	[	[	X
ejpam-3363	41	2	12	12	NUM
ejpam-3363	41	3	,	,	PUNCT
ejpam-3363	41	4	p.111	p.111	ADJ
ejpam-3363	41	5	]	]	PUNCT
ejpam-3363	41	6	.	.	PUNCT
ejpam-3363	42	1	it	it	PRON
ejpam-3363	42	2	is	be	AUX
ejpam-3363	42	3	shown	show	VERB
ejpam-3363	42	4	in	in	ADP
ejpam-3363	42	5	[	[	X
ejpam-3363	42	6	1	1	NUM
ejpam-3363	42	7	,	,	PUNCT
ejpam-3363	42	8	p.25	p.25	NOUN
ejpam-3363	42	9	]	]	PUNCT
ejpam-3363	42	10	that	that	SCONJ
ejpam-3363	42	11	l(u	l(u	PROPN
ejpam-3363	42	12	,	,	PUNCT
ejpam-3363	42	13	v	v	NOUN
ejpam-3363	42	14	)	)	PUNCT
ejpam-3363	42	15	is	be	AUX
ejpam-3363	42	16	properly	properly	ADV
ejpam-3363	42	17	contained	contain	VERB
ejpam-3363	42	18	in	in	ADP
ejpam-3363	42	19	l2(uq	l2(uq	PROPN
ejpam-3363	42	20	,	,	PUNCT
ejpam-3363	42	21	v	v	NOUN
ejpam-3363	42	22	)	)	PUNCT
ejpam-3363	42	23	.	.	PUNCT
ejpam-3363	43	1	we	we	PRON
ejpam-3363	43	2	also	also	ADV
ejpam-3363	43	3	note	note	VERB
ejpam-3363	43	4	that	that	SCONJ
ejpam-3363	43	5	l2(uq	l2(uq	PROPN
ejpam-3363	43	6	,	,	PUNCT
ejpam-3363	43	7	v	v	NOUN
ejpam-3363	43	8	)	)	PUNCT
ejpam-3363	43	9	contains	contain	VERB
ejpam-3363	43	10	genuinely	genuinely	ADV
ejpam-3363	43	11	unbounded	unbounded	ADJ
ejpam-3363	43	12	linear	linear	NOUN
ejpam-3363	43	13	operators	operator	NOUN
ejpam-3363	43	14	from	from	ADP
ejpam-3363	43	15	u	u	PRON
ejpam-3363	43	16	to	to	ADP
ejpam-3363	43	17	v	v	NOUN
ejpam-3363	43	18	.	.	PUNCT
ejpam-3363	44	1	let	let	VERB
ejpam-3363	44	2	q	q	PRON
ejpam-3363	44	3	:	:	PUNCT
ejpam-3363	44	4	u	u	X
ejpam-3363	44	5	→	→	SYM
ejpam-3363	44	6	u	u	X
ejpam-3363	44	7	be	be	VERB
ejpam-3363	44	8	a	a	DET
ejpam-3363	44	9	symmetric	symmetric	ADJ
ejpam-3363	44	10	nonnegative	nonnegative	ADJ
ejpam-3363	44	11	definite	definite	ADJ
ejpam-3363	44	12	trace	trace	NOUN
ejpam-3363	44	13	-	-	PUNCT
ejpam-3363	44	14	class	class	NOUN
ejpam-3363	44	15	operator	operator	NOUN
ejpam-3363	44	16	,	,	PUNCT
ejpam-3363	44	17	{	{	PUNCT
ejpam-3363	44	18	λj	λj	PROPN
ejpam-3363	44	19	,	,	PUNCT
ejpam-3363	44	20	ej	ej	AUX
ejpam-3363	44	21	}	}	PUNCT
ejpam-3363	44	22	be	be	AUX
ejpam-3363	44	23	an	an	DET
ejpam-3363	44	24	eigensequence	eigensequence	NOUN
ejpam-3363	44	25	defined	define	VERB
ejpam-3363	44	26	by	by	ADP
ejpam-3363	44	27	q	q	PROPN
ejpam-3363	44	28	,	,	PUNCT
ejpam-3363	44	29	and	and	CCONJ
ejpam-3363	44	30	{	{	PUNCT
ejpam-3363	44	31	bj	bj	AUX
ejpam-3363	44	32	}	}	PUNCT
ejpam-3363	44	33	be	be	AUX
ejpam-3363	44	34	a	a	DET
ejpam-3363	44	35	sequence	sequence	NOUN
ejpam-3363	44	36	of	of	ADP
ejpam-3363	44	37	independent	independent	ADJ
ejpam-3363	44	38	brownian	brownian	ADJ
ejpam-3363	44	39	motions	motion	NOUN
ejpam-3363	44	40	(	(	PUNCT
ejpam-3363	44	41	abbrev	abbrev	VERB
ejpam-3363	44	42	.	.	PUNCT
ejpam-3363	45	1	as	as	SCONJ
ejpam-3363	45	2	bm	bm	PROPN
ejpam-3363	45	3	)	)	PUNCT
ejpam-3363	45	4	defined	define	VERB
ejpam-3363	45	5	on	on	ADP
ejpam-3363	45	6	(	(	PUNCT
ejpam-3363	45	7	ω	ω	PROPN
ejpam-3363	45	8	,	,	PUNCT
ejpam-3363	45	9	f	f	PROPN
ejpam-3363	45	10	,	,	PUNCT
ejpam-3363	45	11	{	{	PUNCT
ejpam-3363	45	12	ft},p	ft},p	NOUN
ejpam-3363	45	13	)	)	PUNCT
ejpam-3363	45	14	.	.	PUNCT
ejpam-3363	46	1	the	the	DET
ejpam-3363	46	2	process	process	NOUN
ejpam-3363	46	3	w̃t	w̃t	VERB
ejpam-3363	46	4	:	:	PUNCT
ejpam-3363	46	5	=	=	SYM
ejpam-3363	46	6	∞∑	∞∑	NUM
ejpam-3363	46	7	j=1	j=1	NOUN
ejpam-3363	46	8	√	√	NUM
ejpam-3363	46	9	λjbj(t)ej	λjbj(t)ej	NOUN
ejpam-3363	46	10	(	(	PUNCT
ejpam-3363	46	11	1	1	NUM
ejpam-3363	46	12	)	)	PUNCT
ejpam-3363	46	13	is	be	AUX
ejpam-3363	46	14	called	call	VERB
ejpam-3363	46	15	a	a	DET
ejpam-3363	46	16	q	q	ADJ
ejpam-3363	46	17	-	-	PUNCT
ejpam-3363	46	18	wiener	wiener	NOUN
ejpam-3363	46	19	process	process	NOUN
ejpam-3363	46	20	in	in	ADP
ejpam-3363	46	21	u	u	PROPN
ejpam-3363	46	22	.	.	PUNCT
ejpam-3363	47	1	the	the	DET
ejpam-3363	47	2	series	series	NOUN
ejpam-3363	47	3	in	in	ADP
ejpam-3363	47	4	(	(	PUNCT
ejpam-3363	47	5	1	1	X
ejpam-3363	47	6	)	)	PUNCT
ejpam-3363	47	7	converges	converge	NOUN
ejpam-3363	47	8	in	in	ADP
ejpam-3363	47	9	l2(ω	l2(ω	PROPN
ejpam-3363	47	10	,	,	PUNCT
ejpam-3363	47	11	u	u	NOUN
ejpam-3363	47	12	)	)	PUNCT
ejpam-3363	47	13	.	.	PUNCT
ejpam-3363	48	1	for	for	ADP
ejpam-3363	48	2	each	each	DET
ejpam-3363	48	3	u	u	PROPN
ejpam-3363	48	4	∈	∈	PROPN
ejpam-3363	48	5	u	u	NOUN
ejpam-3363	48	6	,	,	PUNCT
ejpam-3363	48	7	denote	denote	NOUN
ejpam-3363	48	8	w̃t(u	w̃t(u	PROPN
ejpam-3363	48	9	)	)	PUNCT
ejpam-3363	49	1	:	:	PUNCT
ejpam-3363	50	1	=	=	PUNCT
ejpam-3363	51	1	∞∑	∞∑	NUM
ejpam-3363	51	2	j=1	j=1	NOUN
ejpam-3363	51	3	√	√	ADP
ejpam-3363	51	4	λjbj(t	λjbj(t	NUM
ejpam-3363	51	5	)	)	PUNCT
ejpam-3363	52	1	〈	〈	PROPN
ejpam-3363	52	2	ej	ej	PROPN
ejpam-3363	52	3	,	,	PUNCT
ejpam-3363	52	4	u〉u	u〉u	PROPN
ejpam-3363	52	5	,	,	PUNCT
ejpam-3363	52	6	with	with	ADP
ejpam-3363	52	7	the	the	DET
ejpam-3363	52	8	series	series	NOUN
ejpam-3363	52	9	converging	converge	VERB
ejpam-3363	52	10	in	in	ADP
ejpam-3363	52	11	l2(ω	l2(ω	PROPN
ejpam-3363	52	12	,	,	PUNCT
ejpam-3363	52	13	r	r	NOUN
ejpam-3363	52	14	)	)	PUNCT
ejpam-3363	52	15	.	.	PUNCT
ejpam-3363	53	1	since	since	SCONJ
ejpam-3363	53	2	the	the	DET
ejpam-3363	53	3	operator	operator	NOUN
ejpam-3363	53	4	q	q	NOUN
ejpam-3363	53	5	is	be	AUX
ejpam-3363	53	6	assumed	assume	VERB
ejpam-3363	53	7	to	to	PART
ejpam-3363	53	8	be	be	AUX
ejpam-3363	53	9	symmetric	symmetric	ADJ
ejpam-3363	53	10	nonnegative	nonnegative	ADJ
ejpam-3363	53	11	definite	definite	ADJ
ejpam-3363	53	12	trace	trace	NOUN
ejpam-3363	53	13	-	-	PUNCT
ejpam-3363	53	14	class	class	NOUN
ejpam-3363	53	15	,	,	PUNCT
ejpam-3363	53	16	there	there	PRON
ejpam-3363	53	17	exists	exist	VERB
ejpam-3363	53	18	a	a	DET
ejpam-3363	53	19	u	u	NOUN
ejpam-3363	53	20	-valued	-value	VERB
ejpam-3363	53	21	process	process	NOUN
ejpam-3363	53	22	w	w	ADP
ejpam-3363	53	23	such	such	ADJ
ejpam-3363	53	24	that	that	DET
ejpam-3363	53	25	w̃t(u)(ω	w̃t(u)(ω	PROPN
ejpam-3363	53	26	)	)	PUNCT
ejpam-3363	54	1	=	=	SYM
ejpam-3363	54	2	〈	〈	PROPN
ejpam-3363	54	3	wt(ω	wt(ω	NOUN
ejpam-3363	54	4	)	)	PUNCT
ejpam-3363	54	5	,	,	PUNCT
ejpam-3363	54	6	u〉u	u〉u	VERB
ejpam-3363	54	7	p	p	NOUN
ejpam-3363	54	8	-	-	PUNCT
ejpam-3363	54	9	almost	almost	ADV
ejpam-3363	54	10	surely	surely	ADV
ejpam-3363	54	11	(	(	PUNCT
ejpam-3363	54	12	abbrev	abbrev	X
ejpam-3363	54	13	.	.	PUNCT
ejpam-3363	55	1	as	as	ADP
ejpam-3363	55	2	p	p	PROPN
ejpam-3363	55	3	-	-	PUNCT
ejpam-3363	55	4	a.s	a.s	PROPN
ejpam-3363	55	5	.	.	PROPN
ejpam-3363	55	6	)	)	PUNCT
ejpam-3363	55	7	.	.	PUNCT
ejpam-3363	56	1	(	(	PUNCT
ejpam-3363	56	2	2	2	X
ejpam-3363	56	3	)	)	PUNCT
ejpam-3363	56	4	we	we	PRON
ejpam-3363	56	5	call	call	VERB
ejpam-3363	56	6	the	the	DET
ejpam-3363	56	7	process	process	NOUN
ejpam-3363	56	8	w	w	ADP
ejpam-3363	56	9	a	a	PRON
ejpam-3363	56	10	u	u	NOUN
ejpam-3363	56	11	-valued	-valued	ADJ
ejpam-3363	56	12	q	q	ADJ
ejpam-3363	56	13	-	-	PUNCT
ejpam-3363	56	14	wiener	wiener	NOUN
ejpam-3363	56	15	process	process	NOUN
ejpam-3363	56	16	.	.	PUNCT
ejpam-3363	57	1	this	this	DET
ejpam-3363	57	2	process	process	NOUN
ejpam-3363	57	3	is	be	AUX
ejpam-3363	57	4	a	a	DET
ejpam-3363	57	5	multidimentional	multidimentional	ADJ
ejpam-3363	57	6	bm	bm	X
ejpam-3363	57	7	.	.	PUNCT
ejpam-3363	58	1	it	it	PRON
ejpam-3363	58	2	should	should	AUX
ejpam-3363	58	3	be	be	AUX
ejpam-3363	58	4	noted	note	VERB
ejpam-3363	58	5	that	that	SCONJ
ejpam-3363	58	6	if	if	SCONJ
ejpam-3363	58	7	we	we	PRON
ejpam-3363	58	8	assume	assume	VERB
ejpam-3363	58	9	that	that	SCONJ
ejpam-3363	58	10	λj	λj	PROPN
ejpam-3363	58	11	>	>	X
ejpam-3363	58	12	0	0	PUNCT
ejpam-3363	58	13	for	for	ADP
ejpam-3363	58	14	all	all	DET
ejpam-3363	58	15	j	j	PROPN
ejpam-3363	58	16	,	,	PUNCT
ejpam-3363	58	17	wt(ej)√	wt(ej)√	NOUN
ejpam-3363	58	18	λj	λj	PROPN
ejpam-3363	58	19	,	,	PUNCT
ejpam-3363	58	20	j	j	PROPN
ejpam-3363	58	21	=	=	SYM
ejpam-3363	58	22	1	1	NUM
ejpam-3363	58	23	,	,	PUNCT
ejpam-3363	58	24	2	2	NUM
ejpam-3363	58	25	,	,	PUNCT
ejpam-3363	58	26	.	.	PUNCT
ejpam-3363	58	27	.	.	PUNCT
ejpam-3363	59	1	.	.	PUNCT
ejpam-3363	60	1	,	,	PUNCT
ejpam-3363	60	2	is	be	AUX
ejpam-3363	60	3	a	a	DET
ejpam-3363	60	4	sequence	sequence	NOUN
ejpam-3363	60	5	of	of	ADP
ejpam-3363	60	6	real	real	ADV
ejpam-3363	60	7	-	-	PUNCT
ejpam-3363	60	8	valued	value	VERB
ejpam-3363	60	9	bm	bm	NOUN
ejpam-3363	60	10	defined	define	VERB
ejpam-3363	60	11	on	on	ADP
ejpam-3363	60	12	(	(	PUNCT
ejpam-3363	60	13	ω	ω	PROPN
ejpam-3363	60	14	,	,	PUNCT
ejpam-3363	60	15	f	f	PROPN
ejpam-3363	60	16	,	,	PUNCT
ejpam-3363	60	17	{	{	PUNCT
ejpam-3363	60	18	ft},p	ft},p	NOUN
ejpam-3363	60	19	)	)	PUNCT
ejpam-3363	60	20	,	,	PUNCT
ejpam-3363	60	21	see	see	VERB
ejpam-3363	60	22	[	[	X
ejpam-3363	60	23	13	13	NUM
ejpam-3363	60	24	,	,	PUNCT
ejpam-3363	60	25	p.87	p.87	PROPN
ejpam-3363	60	26	]	]	PUNCT
ejpam-3363	60	27	.	.	PUNCT
ejpam-3363	61	1	a	a	DET
ejpam-3363	61	2	filtration	filtration	NOUN
ejpam-3363	61	3	{	{	PUNCT
ejpam-3363	61	4	ft	ft	NOUN
ejpam-3363	61	5	}	}	PUNCT
ejpam-3363	61	6	on	on	ADP
ejpam-3363	61	7	a	a	DET
ejpam-3363	61	8	probability	probability	NOUN
ejpam-3363	61	9	space	space	NOUN
ejpam-3363	61	10	(	(	PUNCT
ejpam-3363	61	11	ω	ω	PROPN
ejpam-3363	61	12	,	,	PUNCT
ejpam-3363	61	13	f	f	PROPN
ejpam-3363	61	14	,	,	PUNCT
ejpam-3363	61	15	p	p	NOUN
ejpam-3363	61	16	)	)	PUNCT
ejpam-3363	61	17	is	be	AUX
ejpam-3363	61	18	called	call	VERB
ejpam-3363	61	19	normal	normal	ADJ
ejpam-3363	61	20	if	if	SCONJ
ejpam-3363	61	21	(	(	PUNCT
ejpam-3363	61	22	i	i	NOUN
ejpam-3363	61	23	)	)	PUNCT
ejpam-3363	61	24	f0	f0	PROPN
ejpam-3363	61	25	contains	contain	VERB
ejpam-3363	61	26	all	all	DET
ejpam-3363	61	27	elements	element	NOUN
ejpam-3363	61	28	a	a	DET
ejpam-3363	61	29	∈	∈	NOUN
ejpam-3363	61	30	f	f	NOUN
ejpam-3363	61	31	such	such	ADJ
ejpam-3363	61	32	that	that	DET
ejpam-3363	61	33	p(a	p(a	NOUN
ejpam-3363	61	34	)	)	PUNCT
ejpam-3363	61	35	=	=	SYM
ejpam-3363	61	36	0	0	NUM
ejpam-3363	61	37	,	,	PUNCT
ejpam-3363	61	38	and	and	CCONJ
ejpam-3363	61	39	(	(	PUNCT
ejpam-3363	61	40	ii	ii	NOUN
ejpam-3363	61	41	)	)	PUNCT
ejpam-3363	61	42	ft	ft	NOUN
ejpam-3363	61	43	=	=	PUNCT
ejpam-3363	61	44	ft+	ft+	NOUN
ejpam-3363	61	45	:	:	PUNCT
ejpam-3363	62	1	=	=	SYM
ejpam-3363	62	2	⋂	⋂	PROPN
ejpam-3363	62	3	s	s	X
ejpam-3363	62	4	>	>	X
ejpam-3363	62	5	t	t	X
ejpam-3363	62	6	fs	f	NOUN
ejpam-3363	62	7	for	for	ADP
ejpam-3363	62	8	all	all	DET
ejpam-3363	62	9	t	t	NOUN
ejpam-3363	62	10	∈	∈	PROPN
ejpam-3363	63	1	[	[	X
ejpam-3363	63	2	0	0	NUM
ejpam-3363	63	3	,	,	PUNCT
ejpam-3363	63	4	t	t	X
ejpam-3363	63	5	]	]	PUNCT
ejpam-3363	63	6	.	.	PUNCT
ejpam-3363	64	1	a	a	DET
ejpam-3363	64	2	q	q	ADJ
ejpam-3363	64	3	-	-	PUNCT
ejpam-3363	64	4	wiener	wiener	NOUN
ejpam-3363	64	5	process	process	NOUN
ejpam-3363	64	6	wt	wt	PROPN
ejpam-3363	64	7	,	,	PUNCT
ejpam-3363	64	8	t	t	PROPN
ejpam-3363	64	9	∈	∈	PROPN
ejpam-3363	65	1	[	[	X
ejpam-3363	65	2	0	0	NUM
ejpam-3363	65	3	,	,	PUNCT
ejpam-3363	65	4	t	t	PROPN
ejpam-3363	65	5	]	]	PUNCT
ejpam-3363	65	6	is	be	AUX
ejpam-3363	65	7	called	call	VERB
ejpam-3363	65	8	a	a	DET
ejpam-3363	65	9	q	q	ADJ
ejpam-3363	65	10	-	-	PUNCT
ejpam-3363	65	11	wiener	wiener	NOUN
ejpam-3363	65	12	process	process	NOUN
ejpam-3363	65	13	with	with	ADP
ejpam-3363	65	14	respect	respect	NOUN
ejpam-3363	65	15	to	to	ADP
ejpam-3363	65	16	a	a	DET
ejpam-3363	65	17	filtration	filtration	NOUN
ejpam-3363	65	18	{	{	PUNCT
ejpam-3363	65	19	ft	ft	NOUN
ejpam-3363	65	20	}	}	PUNCT
ejpam-3363	65	21	if	if	SCONJ
ejpam-3363	65	22	(	(	PUNCT
ejpam-3363	65	23	i	i	NOUN
ejpam-3363	65	24	)	)	PUNCT
ejpam-3363	65	25	wt	wt	PROPN
ejpam-3363	65	26	is	be	AUX
ejpam-3363	65	27	adapted	adapt	VERB
ejpam-3363	65	28	to	to	ADP
ejpam-3363	65	29	{	{	PUNCT
ejpam-3363	65	30	ft	ft	X
ejpam-3363	65	31	}	}	PUNCT
ejpam-3363	65	32	,	,	PUNCT
ejpam-3363	65	33	t	t	PROPN
ejpam-3363	65	34	∈	∈	PROPN
ejpam-3363	66	1	[	[	X
ejpam-3363	66	2	0	0	NUM
ejpam-3363	66	3	,	,	PUNCT
ejpam-3363	66	4	t	t	NOUN
ejpam-3363	66	5	]	]	PUNCT
ejpam-3363	66	6	and	and	CCONJ
ejpam-3363	66	7	(	(	PUNCT
ejpam-3363	66	8	ii	ii	NOUN
ejpam-3363	66	9	)	)	PUNCT
ejpam-3363	66	10	wt	wt	ADP
ejpam-3363	66	11	−ws	−ws	PROPN
ejpam-3363	66	12	is	be	AUX
ejpam-3363	66	13	independent	independent	ADJ
ejpam-3363	66	14	of	of	ADP
ejpam-3363	66	15	fs	f	NOUN
ejpam-3363	66	16	for	for	ADP
ejpam-3363	66	17	all	all	DET
ejpam-3363	66	18	0	0	NUM
ejpam-3363	66	19	≤	≤	NUM
ejpam-3363	66	20	s	s	PART
ejpam-3363	66	21	≤	≤	NUM
ejpam-3363	66	22	t	t	NOUN
ejpam-3363	66	23	≤	≤	NOUN
ejpam-3363	66	24	t	t	PROPN
ejpam-3363	66	25	.	.	PUNCT
ejpam-3363	67	1	it	it	PRON
ejpam-3363	67	2	is	be	AUX
ejpam-3363	67	3	shown	show	VERB
ejpam-3363	67	4	in	in	ADP
ejpam-3363	67	5	[	[	X
ejpam-3363	67	6	12	12	NUM
ejpam-3363	67	7	,	,	PUNCT
ejpam-3363	67	8	p.16	p.16	PROPN
ejpam-3363	67	9	]	]	PUNCT
ejpam-3363	67	10	that	that	SCONJ
ejpam-3363	67	11	a	a	DET
ejpam-3363	67	12	u	u	NOUN
ejpam-3363	67	13	-valued	-value	VERB
ejpam-3363	67	14	q	q	ADJ
ejpam-3363	67	15	-	-	PUNCT
ejpam-3363	67	16	wiener	wiener	NOUN
ejpam-3363	67	17	process	process	NOUN
ejpam-3363	67	18	w	w	PROPN
ejpam-3363	67	19	(	(	PUNCT
ejpam-3363	67	20	t	t	PROPN
ejpam-3363	67	21	)	)	PUNCT
ejpam-3363	67	22	,	,	PUNCT
ejpam-3363	67	23	t	t	PROPN
ejpam-3363	67	24	∈	∈	PROPN
ejpam-3363	68	1	[	[	X
ejpam-3363	68	2	0	0	NUM
ejpam-3363	68	3	,	,	PUNCT
ejpam-3363	68	4	t	t	X
ejpam-3363	68	5	]	]	PUNCT
ejpam-3363	68	6	,	,	PUNCT
ejpam-3363	68	7	is	be	AUX
ejpam-3363	68	8	a	a	DET
ejpam-3363	68	9	q	q	ADJ
ejpam-3363	68	10	-	-	PUNCT
ejpam-3363	68	11	wiener	wiener	NOUN
ejpam-3363	68	12	process	process	NOUN
ejpam-3363	68	13	with	with	ADP
ejpam-3363	68	14	respect	respect	NOUN
ejpam-3363	68	15	to	to	ADP
ejpam-3363	68	16	a	a	DET
ejpam-3363	68	17	normal	normal	ADJ
ejpam-3363	68	18	filtration	filtration	NOUN
ejpam-3363	68	19	.	.	PUNCT
ejpam-3363	69	1	from	from	ADP
ejpam-3363	69	2	now	now	ADV
ejpam-3363	69	3	onwards	onward	NOUN
ejpam-3363	69	4	,	,	PUNCT
ejpam-3363	69	5	a	a	DET
ejpam-3363	69	6	filtered	filter	VERB
ejpam-3363	69	7	probability	probability	NOUN
ejpam-3363	69	8	space	space	NOUN
ejpam-3363	69	9	(	(	PUNCT
ejpam-3363	69	10	ω	ω	PROPN
ejpam-3363	69	11	,	,	PUNCT
ejpam-3363	69	12	f	f	PROPN
ejpam-3363	69	13	,	,	PUNCT
ejpam-3363	69	14	{	{	PUNCT
ejpam-3363	69	15	ft},p	ft},p	NOUN
ejpam-3363	69	16	)	)	PUNCT
ejpam-3363	69	17	shall	shall	AUX
ejpam-3363	69	18	mean	mean	VERB
ejpam-3363	69	19	a	a	DET
ejpam-3363	69	20	probability	probability	NOUN
ejpam-3363	69	21	space	space	NOUN
ejpam-3363	69	22	equipped	equip	VERB
ejpam-3363	69	23	with	with	ADP
ejpam-3363	69	24	a	a	DET
ejpam-3363	69	25	normal	normal	ADJ
ejpam-3363	69	26	filtration	filtration	NOUN
ejpam-3363	69	27	.	.	PUNCT
ejpam-3363	70	1	3	3	X
ejpam-3363	70	2	.	.	X
ejpam-3363	70	3	itô-mcshane	itô-mcshane	VERB
ejpam-3363	70	4	integral	integral	ADJ
ejpam-3363	70	5	and	and	CCONJ
ejpam-3363	70	6	belated	belate	VERB
ejpam-3363	70	7	mcshane	mcshane	PROPN
ejpam-3363	70	8	derivative	derivative	NOUN
ejpam-3363	70	9	in	in	ADP
ejpam-3363	70	10	this	this	DET
ejpam-3363	70	11	section	section	NOUN
ejpam-3363	70	12	,	,	PUNCT
ejpam-3363	70	13	we	we	PRON
ejpam-3363	70	14	introduce	introduce	VERB
ejpam-3363	70	15	the	the	DET
ejpam-3363	70	16	itô-mcshane	itô-mcshane	NOUN
ejpam-3363	70	17	integral	integral	ADJ
ejpam-3363	70	18	of	of	ADP
ejpam-3363	70	19	a	a	DET
ejpam-3363	70	20	process	process	NOUN
ejpam-3363	70	21	f	f	NOUN
ejpam-3363	70	22	:	:	PUNCT
ejpam-3363	71	1	[	[	X
ejpam-3363	71	2	0	0	NUM
ejpam-3363	71	3	,	,	PUNCT
ejpam-3363	71	4	t	t	X
ejpam-3363	71	5	]	]	PUNCT
ejpam-3363	71	6	×	×	PROPN
ejpam-3363	71	7	ω	ω	PROPN
ejpam-3363	71	8	→	→	SYM
ejpam-3363	71	9	l(u	l(u	PROPN
ejpam-3363	71	10	,	,	PUNCT
ejpam-3363	71	11	v	v	NOUN
ejpam-3363	71	12	)	)	PUNCT
ejpam-3363	71	13	with	with	ADP
ejpam-3363	71	14	respect	respect	NOUN
ejpam-3363	71	15	to	to	ADP
ejpam-3363	71	16	a	a	DET
ejpam-3363	71	17	u	u	NOUN
ejpam-3363	71	18	-valued	-valued	ADJ
ejpam-3363	71	19	q	q	ADJ
ejpam-3363	71	20	-	-	PUNCT
ejpam-3363	71	21	wiener	wiener	NOUN
ejpam-3363	71	22	process	process	NOUN
ejpam-3363	71	23	w	w	NOUN
ejpam-3363	71	24	and	and	CCONJ
ejpam-3363	71	25	the	the	DET
ejpam-3363	71	26	belated	belate	VERB
ejpam-3363	71	27	mcshane	mcshane	PROPN
ejpam-3363	71	28	derivative	derivative	NOUN
ejpam-3363	71	29	of	of	ADP
ejpam-3363	71	30	a	a	DET
ejpam-3363	71	31	hilbert	hilbert	NOUN
ejpam-3363	71	32	space	space	NOUN
ejpam-3363	71	33	-	-	PUNCT
ejpam-3363	71	34	valued	value	VERB
ejpam-3363	71	35	function	function	NOUN
ejpam-3363	71	36	.	.	PUNCT
ejpam-3363	72	1	throughout	throughout	ADV
ejpam-3363	72	2	,	,	PUNCT
ejpam-3363	72	3	assume	assume	VERB
ejpam-3363	72	4	that	that	SCONJ
ejpam-3363	72	5	u	u	PROPN
ejpam-3363	72	6	and	and	CCONJ
ejpam-3363	72	7	v	v	NOUN
ejpam-3363	72	8	are	be	AUX
ejpam-3363	72	9	separable	separable	ADJ
ejpam-3363	72	10	hilberts	hilbert	NOUN
ejpam-3363	72	11	spaces	space	NOUN
ejpam-3363	72	12	,	,	PUNCT
ejpam-3363	72	13	q	q	NOUN
ejpam-3363	72	14	:	:	PUNCT
ejpam-3363	72	15	u	u	X
ejpam-3363	72	16	→	→	SYM
ejpam-3363	72	17	u	u	PROPN
ejpam-3363	72	18	is	be	AUX
ejpam-3363	72	19	a	a	DET
ejpam-3363	72	20	symmetric	symmetric	ADJ
ejpam-3363	72	21	nonnegative	nonnegative	ADJ
ejpam-3363	72	22	definite	definite	ADJ
ejpam-3363	72	23	trace	trace	NOUN
ejpam-3363	72	24	-	-	PUNCT
ejpam-3363	72	25	class	class	NOUN
ejpam-3363	72	26	operator	operator	NOUN
ejpam-3363	72	27	,	,	PUNCT
ejpam-3363	72	28	{	{	PUNCT
ejpam-3363	72	29	λj	λj	PROPN
ejpam-3363	72	30	,	,	PUNCT
ejpam-3363	72	31	ej	ej	X
ejpam-3363	72	32	}	}	PUNCT
ejpam-3363	72	33	is	be	AUX
ejpam-3363	72	34	an	an	DET
ejpam-3363	72	35	eigensequence	eigensequence	NOUN
ejpam-3363	72	36	defined	define	VERB
ejpam-3363	72	37	by	by	ADP
ejpam-3363	72	38	q	q	PROPN
ejpam-3363	72	39	,	,	PUNCT
ejpam-3363	72	40	and	and	CCONJ
ejpam-3363	72	41	w	w	NOUN
ejpam-3363	72	42	is	be	AUX
ejpam-3363	72	43	a	a	DET
ejpam-3363	72	44	u	u	NOUN
ejpam-3363	72	45	-valued	-valued	ADJ
ejpam-3363	72	46	q	q	ADJ
ejpam-3363	72	47	-	-	PUNCT
ejpam-3363	72	48	wiener	wiener	NOUN
ejpam-3363	72	49	process	process	NOUN
ejpam-3363	72	50	.	.	PUNCT
ejpam-3363	73	1	a	a	DET
ejpam-3363	73	2	stochastic	stochastic	ADJ
ejpam-3363	73	3	process	process	NOUN
ejpam-3363	73	4	f	f	NOUN
ejpam-3363	73	5	:	:	PUNCT
ejpam-3363	74	1	[	[	X
ejpam-3363	74	2	0	0	NUM
ejpam-3363	74	3	,	,	PUNCT
ejpam-3363	74	4	t	t	X
ejpam-3363	74	5	]	]	PUNCT
ejpam-3363	74	6	×	×	PROPN
ejpam-3363	74	7	ω	ω	PROPN
ejpam-3363	74	8	→	→	SYM
ejpam-3363	74	9	l(u	l(u	PROPN
ejpam-3363	74	10	,	,	PUNCT
ejpam-3363	74	11	v	v	NOUN
ejpam-3363	74	12	)	)	PUNCT
ejpam-3363	74	13	means	mean	VERB
ejpam-3363	74	14	a	a	DET
ejpam-3363	74	15	process	process	NOUN
ejpam-3363	74	16	measurable	measurable	ADJ
ejpam-3363	74	17	as	as	ADP
ejpam-3363	74	18	mappings	mapping	NOUN
ejpam-3363	74	19	from	from	ADP
ejpam-3363	74	20	[	[	X
ejpam-3363	74	21	0	0	NUM
ejpam-3363	74	22	,	,	PUNCT
ejpam-3363	74	23	t	t	X
ejpam-3363	74	24	]	]	PUNCT
ejpam-3363	74	25	×	×	PROPN
ejpam-3363	74	26	ω	ω	PROPN
ejpam-3363	74	27	,	,	PUNCT
ejpam-3363	74	28	b([0	b([0	PROPN
ejpam-3363	74	29	,	,	PUNCT
ejpam-3363	74	30	t	t	X
ejpam-3363	74	31	]	]	PUNCT
ejpam-3363	74	32	)	)	PUNCT
ejpam-3363	75	1	⊗	⊗	PROPN
ejpam-3363	75	2	f	f	X
ejpam-3363	75	3	)	)	PUNCT
ejpam-3363	75	4	to	to	ADP
ejpam-3363	75	5	(	(	PUNCT
ejpam-3363	75	6	l2(uq	l2(uq	PROPN
ejpam-3363	75	7	,	,	PUNCT
ejpam-3363	75	8	v	v	NOUN
ejpam-3363	75	9	)	)	PUNCT
ejpam-3363	75	10	,	,	PUNCT
ejpam-3363	75	11	b(l2(uq	b(l2(uq	NOUN
ejpam-3363	75	12	,	,	PUNCT
ejpam-3363	75	13	v	v	NOUN
ejpam-3363	75	14	)	)	PUNCT
ejpam-3363	75	15	)	)	PUNCT
ejpam-3363	75	16	)	)	PUNCT
ejpam-3363	75	17	.	.	PUNCT
ejpam-3363	76	1	also	also	ADV
ejpam-3363	76	2	,	,	PUNCT
ejpam-3363	76	3	the	the	DET
ejpam-3363	76	4	given	give	VERB
ejpam-3363	76	5	closed	closed	ADJ
ejpam-3363	76	6	interval	interval	NOUN
ejpam-3363	76	7	[	[	X
ejpam-3363	76	8	0	0	NUM
ejpam-3363	76	9	,	,	PUNCT
ejpam-3363	76	10	t	t	PROPN
ejpam-3363	76	11	]	]	PUNCT
ejpam-3363	76	12	is	be	AUX
ejpam-3363	76	13	nondegenerate	nondegenerate	ADJ
ejpam-3363	76	14	,	,	PUNCT
ejpam-3363	76	15	i.e.	i.e.	X
ejpam-3363	76	16	0	0	X
ejpam-3363	76	17	<	<	X
ejpam-3363	76	18	t	t	NOUN
ejpam-3363	76	19	and	and	CCONJ
ejpam-3363	76	20	can	can	AUX
ejpam-3363	76	21	be	be	AUX
ejpam-3363	76	22	replaced	replace	VERB
ejpam-3363	76	23	with	with	ADP
ejpam-3363	76	24	any	any	DET
ejpam-3363	76	25	closed	closed	ADJ
ejpam-3363	76	26	interval	interval	NOUN
ejpam-3363	76	27	[	[	X
ejpam-3363	76	28	a	a	X
ejpam-3363	76	29	,	,	PUNCT
ejpam-3363	76	30	b	b	NOUN
ejpam-3363	76	31	]	]	X
ejpam-3363	76	32	.	.	PUNCT
ejpam-3363	77	1	if	if	SCONJ
ejpam-3363	77	2	no	no	DET
ejpam-3363	77	3	confusion	confusion	NOUN
ejpam-3363	77	4	arises	arise	VERB
ejpam-3363	77	5	,	,	PUNCT
ejpam-3363	77	6	we	we	PRON
ejpam-3363	77	7	may	may	AUX
ejpam-3363	77	8	write	write	VERB
ejpam-3363	77	9	(	(	PUNCT
ejpam-3363	77	10	d	d	PROPN
ejpam-3363	77	11	)	)	PUNCT
ejpam-3363	77	12	∑	∑	ADP
ejpam-3363	77	13	instead	instead	ADV
ejpam-3363	77	14	of	of	ADP
ejpam-3363	77	15	n∑	n∑	PROPN
ejpam-3363	77	16	i=1	i=1	PROPN
ejpam-3363	77	17	for	for	ADP
ejpam-3363	77	18	the	the	DET
ejpam-3363	77	19	given	give	VERB
ejpam-3363	77	20	finite	finite	ADJ
ejpam-3363	77	21	collection	collection	PROPN
ejpam-3363	77	22	d.	d.	PROPN
ejpam-3363	77	23	j.d	j.d	PROPN
ejpam-3363	77	24	.	.	PROPN
ejpam-3363	77	25	cagubcob	cagubcob	PROPN
ejpam-3363	77	26	,	,	PUNCT
ejpam-3363	77	27	m.	m.	NOUN
ejpam-3363	77	28	labendia	labendia	PROPN
ejpam-3363	77	29	/	/	SYM
ejpam-3363	77	30	eur	eur	PROPN
ejpam-3363	77	31	.	.	PUNCT
ejpam-3363	78	1	j.	j.	PROPN
ejpam-3363	78	2	pure	pure	PROPN
ejpam-3363	78	3	appl	appl	PROPN
ejpam-3363	78	4	.	.	PROPN
ejpam-3363	78	5	math	math	PROPN
ejpam-3363	78	6	,	,	PUNCT
ejpam-3363	78	7	12	12	NUM
ejpam-3363	78	8	(	(	PUNCT
ejpam-3363	78	9	1	1	NUM
ejpam-3363	78	10	)	)	PUNCT
ejpam-3363	78	11	(	(	PUNCT
ejpam-3363	78	12	2019	2019	NUM
ejpam-3363	78	13	)	)	PUNCT
ejpam-3363	78	14	,	,	PUNCT
ejpam-3363	78	15	101	101	NUM
ejpam-3363	78	16	-	-	SYM
ejpam-3363	78	17	117	117	NUM
ejpam-3363	78	18	104	104	NUM
ejpam-3363	78	19	definition	definition	NOUN
ejpam-3363	78	20	1	1	NUM
ejpam-3363	78	21	.	.	PUNCT
ejpam-3363	79	1	let	let	VERB
ejpam-3363	79	2	δ	δ	PRON
ejpam-3363	79	3	be	be	AUX
ejpam-3363	79	4	a	a	DET
ejpam-3363	79	5	positive	positive	ADJ
ejpam-3363	79	6	function	function	NOUN
ejpam-3363	79	7	defined	define	VERB
ejpam-3363	79	8	on	on	ADP
ejpam-3363	79	9	[	[	X
ejpam-3363	79	10	0	0	NUM
ejpam-3363	79	11	,	,	PUNCT
ejpam-3363	79	12	t	t	X
ejpam-3363	79	13	]	]	PUNCT
ejpam-3363	79	14	.	.	PUNCT
ejpam-3363	80	1	a	a	DET
ejpam-3363	80	2	finite	finite	ADJ
ejpam-3363	80	3	collection	collection	NOUN
ejpam-3363	80	4	d	d	NOUN
ejpam-3363	80	5	=	=	PRON
ejpam-3363	80	6	{	{	PUNCT
ejpam-3363	80	7	(	(	PUNCT
ejpam-3363	80	8	[	[	X
ejpam-3363	80	9	ui	ui	NOUN
ejpam-3363	80	10	,	,	PUNCT
ejpam-3363	80	11	vi	vi	PROPN
ejpam-3363	80	12	]	]	PUNCT
ejpam-3363	80	13	,	,	PUNCT
ejpam-3363	80	14	ξi)}ni=1	ξi)}ni=1	PROPN
ejpam-3363	80	15	of	of	ADP
ejpam-3363	80	16	interval	interval	NOUN
ejpam-3363	80	17	-	-	PUNCT
ejpam-3363	80	18	point	point	NOUN
ejpam-3363	80	19	pairs	pair	NOUN
ejpam-3363	80	20	is	be	AUX
ejpam-3363	80	21	a	a	DET
ejpam-3363	80	22	(	(	PUNCT
ejpam-3363	80	23	iii	iii	NOUN
ejpam-3363	80	24	)	)	PUNCT
ejpam-3363	80	25	δ	δ	NOUN
ejpam-3363	80	26	-	-	PUNCT
ejpam-3363	80	27	fine	fine	PROPN
ejpam-3363	80	28	belated	belate	VERB
ejpam-3363	80	29	mcshane	mcshane	PROPN
ejpam-3363	80	30	division	division	NOUN
ejpam-3363	80	31	of	of	ADP
ejpam-3363	80	32	[	[	X
ejpam-3363	80	33	0	0	NUM
ejpam-3363	80	34	,	,	PUNCT
ejpam-3363	80	35	t	t	X
ejpam-3363	80	36	]	]	PUNCT
ejpam-3363	80	37	if	if	SCONJ
ejpam-3363	80	38	{	{	PUNCT
ejpam-3363	80	39	[	[	X
ejpam-3363	80	40	ui	ui	NOUN
ejpam-3363	80	41	,	,	PUNCT
ejpam-3363	80	42	vi]}ni=1	vi]}ni=1	PROPN
ejpam-3363	80	43	is	be	AUX
ejpam-3363	80	44	a	a	DET
ejpam-3363	80	45	collection	collection	NOUN
ejpam-3363	80	46	of	of	ADP
ejpam-3363	80	47	non	non	ADJ
ejpam-3363	80	48	-	-	ADJ
ejpam-3363	80	49	overlapping	overlapping	ADJ
ejpam-3363	80	50	intervals	interval	NOUN
ejpam-3363	80	51	on	on	ADP
ejpam-3363	80	52	[	[	X
ejpam-3363	80	53	0	0	NUM
ejpam-3363	80	54	,	,	PUNCT
ejpam-3363	80	55	t	t	X
ejpam-3363	80	56	]	]	PUNCT
ejpam-3363	80	57	with	with	ADP
ejpam-3363	80	58	n⋃	n⋃	PROPN
ejpam-3363	80	59	i=1	i=1	PROPN
ejpam-3363	81	1	[	[	X
ejpam-3363	81	2	ui	ui	PROPN
ejpam-3363	81	3	,	,	PUNCT
ejpam-3363	81	4	vi	vi	X
ejpam-3363	81	5	]	]	PUNCT
ejpam-3363	81	6	=	=	PUNCT
ejpam-3363	82	1	[	[	X
ejpam-3363	82	2	0	0	NUM
ejpam-3363	82	3	,	,	PUNCT
ejpam-3363	82	4	t	t	NOUN
ejpam-3363	82	5	]	]	PUNCT
ejpam-3363	82	6	and	and	CCONJ
ejpam-3363	82	7	each	each	DET
ejpam-3363	82	8	[	[	X
ejpam-3363	82	9	ui	ui	PROPN
ejpam-3363	82	10	,	,	PUNCT
ejpam-3363	82	11	vi	vi	PROPN
ejpam-3363	82	12	]	]	X
ejpam-3363	82	13	is	be	AUX
ejpam-3363	82	14	δ	δ	PROPN
ejpam-3363	82	15	-	-	PUNCT
ejpam-3363	82	16	fine	fine	ADJ
ejpam-3363	82	17	belated	belate	VERB
ejpam-3363	82	18	mcshane	mcshane	PROPN
ejpam-3363	82	19	,	,	PUNCT
ejpam-3363	82	20	that	that	ADV
ejpam-3363	82	21	is	is	ADV
ejpam-3363	82	22	,	,	PUNCT
ejpam-3363	82	23	[	[	X
ejpam-3363	82	24	ui	ui	NOUN
ejpam-3363	82	25	,	,	PUNCT
ejpam-3363	82	26	vi	vi	X
ejpam-3363	82	27	]	]	X
ejpam-3363	82	28	⊂	⊂	X
ejpam-3363	83	1	[	[	X
ejpam-3363	83	2	ξi	ξi	NOUN
ejpam-3363	83	3	,	,	PUNCT
ejpam-3363	83	4	ξi	ξi	NOUN
ejpam-3363	83	5	+	+	CCONJ
ejpam-3363	83	6	δ(ξi	δ(ξi	NOUN
ejpam-3363	83	7	)	)	PUNCT
ejpam-3363	83	8	)	)	PUNCT
ejpam-3363	83	9	(	(	PUNCT
ejpam-3363	83	10	iv	iv	X
ejpam-3363	83	11	)	)	PUNCT
ejpam-3363	83	12	δ	δ	NOUN
ejpam-3363	83	13	-	-	PUNCT
ejpam-3363	83	14	fine	fine	PROPN
ejpam-3363	83	15	belated	belate	VERB
ejpam-3363	83	16	mcshane	mcshane	PROPN
ejpam-3363	83	17	partial	partial	ADJ
ejpam-3363	83	18	division	division	NOUN
ejpam-3363	83	19	of	of	ADP
ejpam-3363	83	20	[	[	X
ejpam-3363	83	21	0	0	NUM
ejpam-3363	83	22	,	,	PUNCT
ejpam-3363	83	23	t	t	X
ejpam-3363	83	24	]	]	PUNCT
ejpam-3363	83	25	if	if	SCONJ
ejpam-3363	83	26	{	{	PUNCT
ejpam-3363	83	27	[	[	X
ejpam-3363	83	28	ui	ui	NOUN
ejpam-3363	83	29	,	,	PUNCT
ejpam-3363	83	30	vi]}ni=1	vi]}ni=1	PROPN
ejpam-3363	83	31	is	be	AUX
ejpam-3363	83	32	a	a	DET
ejpam-3363	83	33	collection	collection	NOUN
ejpam-3363	83	34	of	of	ADP
ejpam-3363	83	35	nonoverlapping	nonoverlapping	ADJ
ejpam-3363	83	36	intervals	interval	NOUN
ejpam-3363	83	37	on	on	ADP
ejpam-3363	83	38	[	[	X
ejpam-3363	83	39	0	0	NUM
ejpam-3363	83	40	,	,	PUNCT
ejpam-3363	83	41	t	t	NOUN
ejpam-3363	83	42	]	]	PUNCT
ejpam-3363	83	43	and	and	CCONJ
ejpam-3363	84	1	each	each	DET
ejpam-3363	84	2	[	[	X
ejpam-3363	84	3	ui	ui	PROPN
ejpam-3363	84	4	,	,	PUNCT
ejpam-3363	84	5	vi	vi	PROPN
ejpam-3363	84	6	]	]	X
ejpam-3363	84	7	is	be	AUX
ejpam-3363	84	8	δ	δ	PROPN
ejpam-3363	84	9	-	-	PUNCT
ejpam-3363	84	10	fine	fine	ADJ
ejpam-3363	84	11	belated	belate	VERB
ejpam-3363	84	12	mcshane	mcshane	NOUN
ejpam-3363	84	13	.	.	PUNCT
ejpam-3363	85	1	we	we	PRON
ejpam-3363	85	2	note	note	VERB
ejpam-3363	85	3	that	that	SCONJ
ejpam-3363	85	4	each	each	DET
ejpam-3363	85	5	ξi	ξi	NOUN
ejpam-3363	85	6	in	in	ADP
ejpam-3363	85	7	definition	definition	NOUN
ejpam-3363	85	8	1	1	NUM
ejpam-3363	85	9	does	do	AUX
ejpam-3363	85	10	not	not	PART
ejpam-3363	85	11	necessarily	necessarily	ADV
ejpam-3363	85	12	belong	belong	VERB
ejpam-3363	85	13	to	to	ADP
ejpam-3363	85	14	[	[	X
ejpam-3363	85	15	ui	ui	PROPN
ejpam-3363	85	16	,	,	PUNCT
ejpam-3363	85	17	vi	vi	PROPN
ejpam-3363	85	18	]	]	PUNCT
ejpam-3363	85	19	.	.	PUNCT
ejpam-3363	86	1	the	the	DET
ejpam-3363	86	2	term	term	NOUN
ejpam-3363	86	3	partial	partial	ADJ
ejpam-3363	86	4	division	division	NOUN
ejpam-3363	86	5	is	be	AUX
ejpam-3363	86	6	used	use	VERB
ejpam-3363	86	7	in	in	ADP
ejpam-3363	86	8	definition	definition	NOUN
ejpam-3363	86	9	1	1	NUM
ejpam-3363	86	10	since	since	SCONJ
ejpam-3363	86	11	the	the	DET
ejpam-3363	86	12	finite	finite	ADJ
ejpam-3363	86	13	collection	collection	NOUN
ejpam-3363	86	14	of	of	ADP
ejpam-3363	86	15	non	non	ADJ
ejpam-3363	86	16	-	-	ADJ
ejpam-3363	86	17	overlapping	overlapping	ADJ
ejpam-3363	86	18	intervals	interval	NOUN
ejpam-3363	86	19	of	of	ADP
ejpam-3363	86	20	[	[	X
ejpam-3363	86	21	0	0	NUM
ejpam-3363	86	22	,	,	PUNCT
ejpam-3363	86	23	t	t	PROPN
ejpam-3363	86	24	]	]	PUNCT
ejpam-3363	86	25	may	may	AUX
ejpam-3363	86	26	not	not	PART
ejpam-3363	86	27	cover	cover	VERB
ejpam-3363	86	28	the	the	DET
ejpam-3363	86	29	entire	entire	ADJ
ejpam-3363	86	30	interval	interval	NOUN
ejpam-3363	86	31	[	[	X
ejpam-3363	86	32	0	0	NUM
ejpam-3363	86	33	,	,	PUNCT
ejpam-3363	86	34	t	t	X
ejpam-3363	86	35	]	]	PUNCT
ejpam-3363	86	36	.	.	PUNCT
ejpam-3363	87	1	definition	definition	NOUN
ejpam-3363	87	2	2	2	NUM
ejpam-3363	87	3	.	.	PUNCT
ejpam-3363	87	4	given	give	VERB
ejpam-3363	87	5	η	η	PROPN
ejpam-3363	87	6	>	>	X
ejpam-3363	87	7	0	0	PROPN
ejpam-3363	87	8	,	,	PUNCT
ejpam-3363	87	9	a	a	DET
ejpam-3363	87	10	given	give	VERB
ejpam-3363	87	11	δ	δ	NOUN
ejpam-3363	87	12	-	-	PUNCT
ejpam-3363	87	13	fine	fine	NOUN
ejpam-3363	87	14	belated	belate	VERB
ejpam-3363	87	15	mcshane	mcshane	PROPN
ejpam-3363	87	16	partial	partial	ADJ
ejpam-3363	87	17	divisiond	divisiond	NOUN
ejpam-3363	87	18	=	=	PRON
ejpam-3363	87	19	{	{	PUNCT
ejpam-3363	87	20	(	(	PUNCT
ejpam-3363	87	21	[	[	X
ejpam-3363	87	22	u	u	NOUN
ejpam-3363	87	23	,	,	PUNCT
ejpam-3363	87	24	v	v	ADP
ejpam-3363	87	25	]	]	X
ejpam-3363	87	26	,	,	PUNCT
ejpam-3363	87	27	ξ	ξ	X
ejpam-3363	87	28	)	)	PUNCT
ejpam-3363	87	29	}	}	PUNCT
ejpam-3363	87	30	is	be	AUX
ejpam-3363	87	31	said	say	VERB
ejpam-3363	87	32	to	to	PART
ejpam-3363	87	33	be	be	AUX
ejpam-3363	87	34	a	a	DET
ejpam-3363	87	35	(	(	PUNCT
ejpam-3363	87	36	δ	δ	PROPN
ejpam-3363	87	37	,	,	PUNCT
ejpam-3363	87	38	η)-fine	η)-fine	PROPN
ejpam-3363	87	39	belated	belate	VERB
ejpam-3363	87	40	mcshane	mcshane	PROPN
ejpam-3363	87	41	partial	partial	ADJ
ejpam-3363	87	42	division	division	NOUN
ejpam-3363	87	43	of	of	ADP
ejpam-3363	87	44	[	[	X
ejpam-3363	87	45	0	0	NUM
ejpam-3363	87	46	,	,	PUNCT
ejpam-3363	87	47	t	t	X
ejpam-3363	87	48	]	]	PUNCT
ejpam-3363	87	49	if	if	SCONJ
ejpam-3363	87	50	it	it	PRON
ejpam-3363	87	51	fails	fail	VERB
ejpam-3363	87	52	to	to	PART
ejpam-3363	87	53	cover	cover	VERB
ejpam-3363	87	54	[	[	X
ejpam-3363	87	55	0	0	NUM
ejpam-3363	87	56	,	,	PUNCT
ejpam-3363	87	57	t	t	X
ejpam-3363	87	58	]	]	PUNCT
ejpam-3363	87	59	by	by	ADP
ejpam-3363	87	60	at	at	ADP
ejpam-3363	87	61	most	most	ADJ
ejpam-3363	87	62	length	length	NOUN
ejpam-3363	87	63	η	η	PROPN
ejpam-3363	87	64	,	,	PUNCT
ejpam-3363	87	65	that	that	ADV
ejpam-3363	87	66	is	be	AUX
ejpam-3363	87	67	,	,	PUNCT
ejpam-3363	87	68	∣∣∣t	∣∣∣t	NOUN
ejpam-3363	87	69	−	−	PROPN
ejpam-3363	87	70	(	(	PUNCT
ejpam-3363	87	71	d	d	NOUN
ejpam-3363	87	72	)	)	PUNCT
ejpam-3363	87	73	∑	∑	PUNCT
ejpam-3363	87	74	(	(	PUNCT
ejpam-3363	87	75	v	v	ADP
ejpam-3363	87	76	−	−	PROPN
ejpam-3363	87	77	u	u	NOUN
ejpam-3363	87	78	)	)	PUNCT
ejpam-3363	87	79	∣∣∣	∣∣∣	NOUN
ejpam-3363	87	80	≤	≤	PROPN
ejpam-3363	87	81	η	η	PROPN
ejpam-3363	87	82	.	.	PROPN
ejpam-3363	87	83	to	to	PART
ejpam-3363	87	84	define	define	VERB
ejpam-3363	87	85	the	the	DET
ejpam-3363	87	86	itô-mcshane	itô-mcshane	NOUN
ejpam-3363	87	87	integral	integral	ADJ
ejpam-3363	87	88	,	,	PUNCT
ejpam-3363	87	89	we	we	PRON
ejpam-3363	87	90	shall	shall	AUX
ejpam-3363	87	91	use	use	VERB
ejpam-3363	87	92	the	the	DET
ejpam-3363	87	93	definition	definition	NOUN
ejpam-3363	87	94	of	of	ADP
ejpam-3363	87	95	belated	belate	VERB
ejpam-3363	87	96	partial	partial	ADJ
ejpam-3363	87	97	division	division	NOUN
ejpam-3363	87	98	in	in	ADP
ejpam-3363	87	99	definition	definition	NOUN
ejpam-3363	87	100	1	1	NUM
ejpam-3363	87	101	,	,	PUNCT
ejpam-3363	87	102	employed	employ	VERB
ejpam-3363	87	103	by	by	ADP
ejpam-3363	87	104	the	the	DET
ejpam-3363	87	105	authors	author	NOUN
ejpam-3363	87	106	in	in	ADP
ejpam-3363	87	107	[	[	X
ejpam-3363	87	108	17	17	NUM
ejpam-3363	87	109	,	,	PUNCT
ejpam-3363	87	110	p.499	p.499	NOUN
ejpam-3363	87	111	]	]	PUNCT
ejpam-3363	87	112	.	.	PUNCT
ejpam-3363	88	1	definition	definition	NOUN
ejpam-3363	88	2	3	3	X
ejpam-3363	88	3	.	.	PUNCT
ejpam-3363	89	1	let	let	VERB
ejpam-3363	89	2	f	f	NOUN
ejpam-3363	89	3	:	:	PUNCT
ejpam-3363	90	1	[	[	X
ejpam-3363	90	2	0	0	NUM
ejpam-3363	90	3	,	,	PUNCT
ejpam-3363	90	4	t	t	X
ejpam-3363	90	5	]	]	PUNCT
ejpam-3363	90	6	×	×	PROPN
ejpam-3363	90	7	ω	ω	PROPN
ejpam-3363	90	8	→	→	SYM
ejpam-3363	90	9	l(u	l(u	PROPN
ejpam-3363	90	10	,	,	PUNCT
ejpam-3363	90	11	v	v	NOUN
ejpam-3363	90	12	)	)	PUNCT
ejpam-3363	90	13	be	be	AUX
ejpam-3363	90	14	an	an	DET
ejpam-3363	90	15	adapted	adapt	VERB
ejpam-3363	90	16	process	process	NOUN
ejpam-3363	90	17	.	.	PUNCT
ejpam-3363	91	1	then	then	ADV
ejpam-3363	91	2	f	f	PROPN
ejpam-3363	91	3	is	be	AUX
ejpam-3363	91	4	said	say	VERB
ejpam-3363	91	5	to	to	PART
ejpam-3363	91	6	be	be	AUX
ejpam-3363	91	7	itô-mcshane	itô-mcshane	PRON
ejpam-3363	91	8	integrable	integrable	ADJ
ejpam-3363	91	9	,	,	PUNCT
ejpam-3363	91	10	or	or	CCONJ
ejpam-3363	91	11	im	im	ADV
ejpam-3363	91	12	-	-	ADJ
ejpam-3363	91	13	integrable	integrable	ADJ
ejpam-3363	91	14	,	,	PUNCT
ejpam-3363	91	15	on	on	ADP
ejpam-3363	91	16	[	[	X
ejpam-3363	91	17	0	0	NUM
ejpam-3363	91	18	,	,	PUNCT
ejpam-3363	91	19	t	t	X
ejpam-3363	91	20	]	]	PUNCT
ejpam-3363	91	21	with	with	ADP
ejpam-3363	91	22	respect	respect	NOUN
ejpam-3363	91	23	to	to	ADP
ejpam-3363	91	24	w	w	NOUN
ejpam-3363	91	25	if	if	SCONJ
ejpam-3363	91	26	there	there	PRON
ejpam-3363	91	27	exists	exist	VERB
ejpam-3363	91	28	a	a	DET
ejpam-3363	91	29	∈	∈	PROPN
ejpam-3363	91	30	l2(ω	l2(ω	PROPN
ejpam-3363	91	31	,	,	PUNCT
ejpam-3363	91	32	v	v	NOUN
ejpam-3363	91	33	)	)	PUNCT
ejpam-3363	91	34	such	such	ADJ
ejpam-3363	91	35	that	that	PRON
ejpam-3363	91	36	for	for	ADP
ejpam-3363	91	37	every	every	DET
ejpam-3363	91	38	ε	ε	PROPN
ejpam-3363	91	39	>	>	X
ejpam-3363	91	40	0	0	PROPN
ejpam-3363	91	41	,	,	PUNCT
ejpam-3363	91	42	there	there	PRON
ejpam-3363	91	43	is	be	VERB
ejpam-3363	91	44	a	a	DET
ejpam-3363	91	45	positive	positive	ADJ
ejpam-3363	91	46	function	function	NOUN
ejpam-3363	91	47	δ	δ	PROPN
ejpam-3363	91	48	on	on	ADP
ejpam-3363	91	49	[	[	X
ejpam-3363	91	50	0	0	NUM
ejpam-3363	91	51	,	,	PUNCT
ejpam-3363	91	52	t	t	NOUN
ejpam-3363	91	53	]	]	PUNCT
ejpam-3363	91	54	and	and	CCONJ
ejpam-3363	91	55	a	a	DET
ejpam-3363	91	56	number	number	NOUN
ejpam-3363	91	57	η	η	X
ejpam-3363	91	58	>	>	X
ejpam-3363	91	59	0	0	NUM
ejpam-3363	91	60	such	such	ADJ
ejpam-3363	91	61	that	that	PRON
ejpam-3363	91	62	for	for	ADP
ejpam-3363	91	63	any	any	DET
ejpam-3363	91	64	(	(	PUNCT
ejpam-3363	91	65	δ	δ	PROPN
ejpam-3363	91	66	,	,	PUNCT
ejpam-3363	91	67	η)-fine	η)-fine	PROPN
ejpam-3363	91	68	belated	belate	VERB
ejpam-3363	91	69	mcshane	mcshane	PROPN
ejpam-3363	91	70	partial	partial	ADJ
ejpam-3363	91	71	division	division	NOUN
ejpam-3363	91	72	d	d	NOUN
ejpam-3363	91	73	=	=	PRON
ejpam-3363	91	74	{	{	PUNCT
ejpam-3363	91	75	(	(	PUNCT
ejpam-3363	91	76	[	[	X
ejpam-3363	91	77	ui	ui	NOUN
ejpam-3363	91	78	,	,	PUNCT
ejpam-3363	91	79	vi	vi	PROPN
ejpam-3363	91	80	]	]	PUNCT
ejpam-3363	91	81	,	,	PUNCT
ejpam-3363	91	82	ξi)}ni=1	ξi)}ni=1	NOUN
ejpam-3363	91	83	of	of	ADP
ejpam-3363	91	84	[	[	X
ejpam-3363	91	85	0	0	NUM
ejpam-3363	91	86	,	,	PUNCT
ejpam-3363	91	87	t	t	X
ejpam-3363	91	88	]	]	PUNCT
ejpam-3363	91	89	,	,	PUNCT
ejpam-3363	91	90	we	we	PRON
ejpam-3363	91	91	have	have	VERB
ejpam-3363	91	92	e	e	X
ejpam-3363	91	93	[	[	PUNCT
ejpam-3363	91	94	‖s(f	‖s(f	ADJ
ejpam-3363	91	95	,	,	PUNCT
ejpam-3363	91	96	d	d	PROPN
ejpam-3363	91	97	,	,	PUNCT
ejpam-3363	91	98	δ	δ	PROPN
ejpam-3363	91	99	,	,	PUNCT
ejpam-3363	91	100	η)−a‖2v	η)−a‖2v	PROPN
ejpam-3363	91	101	]	]	PUNCT
ejpam-3363	91	102	<	<	X
ejpam-3363	91	103	ε	ε	PROPN
ejpam-3363	91	104	,	,	PUNCT
ejpam-3363	91	105	where	where	SCONJ
ejpam-3363	91	106	s(f	s(f	PROPN
ejpam-3363	91	107	,	,	PUNCT
ejpam-3363	91	108	d	d	PROPN
ejpam-3363	91	109	,	,	PUNCT
ejpam-3363	91	110	δ	δ	PROPN
ejpam-3363	91	111	,	,	PUNCT
ejpam-3363	91	112	η	η	PROPN
ejpam-3363	91	113	)	)	PUNCT
ejpam-3363	91	114	:	:	PUNCT
ejpam-3363	91	115	=	=	SYM
ejpam-3363	91	116	(	(	PUNCT
ejpam-3363	91	117	d	d	NOUN
ejpam-3363	91	118	)	)	PUNCT
ejpam-3363	91	119	∑	∑	PUNCT
ejpam-3363	91	120	fξ(wv	fξ(wv	NOUN
ejpam-3363	91	121	−wu	−wu	NOUN
ejpam-3363	91	122	)	)	PUNCT
ejpam-3363	91	123	:	:	PUNCT
ejpam-3363	92	1	=	=	PUNCT
ejpam-3363	92	2	n∑	n∑	PROPN
ejpam-3363	92	3	i=1	i=1	PROPN
ejpam-3363	92	4	fξi(wvi	fξi(wvi	NOUN
ejpam-3363	92	5	−wui	−wui	X
ejpam-3363	92	6	)	)	PUNCT
ejpam-3363	92	7	.	.	PUNCT
ejpam-3363	93	1	in	in	ADP
ejpam-3363	93	2	this	this	DET
ejpam-3363	93	3	case	case	NOUN
ejpam-3363	93	4	,	,	PUNCT
ejpam-3363	93	5	f	f	PROPN
ejpam-3363	93	6	is	be	AUX
ejpam-3363	93	7	im	im	ADV
ejpam-3363	93	8	-	-	PUNCT
ejpam-3363	93	9	integrable	integrable	ADJ
ejpam-3363	93	10	to	to	ADP
ejpam-3363	93	11	a	a	PRON
ejpam-3363	93	12	on	on	ADP
ejpam-3363	93	13	[	[	X
ejpam-3363	93	14	0	0	NUM
ejpam-3363	93	15	,	,	PUNCT
ejpam-3363	93	16	t	t	NOUN
ejpam-3363	93	17	]	]	PUNCT
ejpam-3363	93	18	and	and	CCONJ
ejpam-3363	93	19	a	a	PRON
ejpam-3363	93	20	is	be	AUX
ejpam-3363	93	21	called	call	VERB
ejpam-3363	93	22	the	the	DET
ejpam-3363	93	23	im	im	ADV
ejpam-3363	93	24	-	-	ADJ
ejpam-3363	93	25	integral	integral	ADJ
ejpam-3363	93	26	of	of	ADP
ejpam-3363	93	27	f	f	PRON
ejpam-3363	93	28	which	which	PRON
ejpam-3363	93	29	will	will	AUX
ejpam-3363	93	30	be	be	AUX
ejpam-3363	93	31	denoted	denote	VERB
ejpam-3363	93	32	by	by	ADP
ejpam-3363	93	33	(	(	PUNCT
ejpam-3363	93	34	i	i	NOUN
ejpam-3363	93	35	m	m	PROPN
ejpam-3363	93	36	)	)	PUNCT
ejpam-3363	94	1	∫	∫	PROPN
ejpam-3363	94	2	t	t	PROPN
ejpam-3363	94	3	0	0	NUM
ejpam-3363	94	4	ft	ft	NOUN
ejpam-3363	94	5	dwt	dwt	NOUN
ejpam-3363	94	6	or	or	CCONJ
ejpam-3363	94	7	(	(	PUNCT
ejpam-3363	94	8	i	i	NOUN
ejpam-3363	94	9	m	m	PROPN
ejpam-3363	94	10	)	)	PUNCT
ejpam-3363	95	1	∫	∫	PROPN
ejpam-3363	95	2	t	t	PROPN
ejpam-3363	95	3	0	0	NUM
ejpam-3363	96	1	f	f	PROPN
ejpam-3363	96	2	dw	dw	PROPN
ejpam-3363	96	3	.	.	PUNCT
ejpam-3363	97	1	we	we	PRON
ejpam-3363	97	2	shall	shall	AUX
ejpam-3363	97	3	denote	denote	VERB
ejpam-3363	97	4	(	(	PUNCT
ejpam-3363	97	5	i	i	NOUN
ejpam-3363	97	6	m	m	VERB
ejpam-3363	97	7	)	)	PUNCT
ejpam-3363	97	8	∫	∫	PROPN
ejpam-3363	97	9	0	0	NUM
ejpam-3363	97	10	0	0	NUM
ejpam-3363	98	1	f	f	X
ejpam-3363	98	2	dw	dw	PROPN
ejpam-3363	98	3	by	by	ADP
ejpam-3363	98	4	the	the	DET
ejpam-3363	98	5	zero	zero	NUM
ejpam-3363	98	6	random	random	ADJ
ejpam-3363	98	7	variable	variable	NOUN
ejpam-3363	98	8	0	0	NUM
ejpam-3363	98	9	from	from	ADP
ejpam-3363	98	10	ω	ω	NUM
ejpam-3363	98	11	to	to	ADP
ejpam-3363	98	12	v	v	NOUN
ejpam-3363	98	13	and	and	CCONJ
ejpam-3363	98	14	denote	denote	VERB
ejpam-3363	98	15	by	by	ADP
ejpam-3363	98	16	λim	λim	PROPN
ejpam-3363	98	17	,	,	PUNCT
ejpam-3363	98	18	the	the	DET
ejpam-3363	98	19	collection	collection	NOUN
ejpam-3363	98	20	of	of	ADP
ejpam-3363	98	21	all	all	PRON
ejpam-3363	98	22	itô-mcshane	itô-mcshane	VERB
ejpam-3363	98	23	integrable	integrable	ADJ
ejpam-3363	98	24	processes	process	NOUN
ejpam-3363	98	25	on	on	ADP
ejpam-3363	98	26	[	[	X
ejpam-3363	98	27	0	0	NUM
ejpam-3363	98	28	,	,	PUNCT
ejpam-3363	98	29	t	t	X
ejpam-3363	98	30	]	]	PUNCT
ejpam-3363	98	31	.	.	PUNCT
ejpam-3363	99	1	refer	refer	VERB
ejpam-3363	99	2	to	to	ADP
ejpam-3363	99	3	[	[	X
ejpam-3363	99	4	6	6	NUM
ejpam-3363	99	5	,	,	PUNCT
ejpam-3363	99	6	lemma	lemma	PROPN
ejpam-3363	99	7	3.5	3.5	NUM
ejpam-3363	99	8	and	and	CCONJ
ejpam-3363	99	9	lemma	lemma	PROPN
ejpam-3363	99	10	3.6	3.6	NUM
ejpam-3363	99	11	]	]	PUNCT
ejpam-3363	99	12	for	for	ADP
ejpam-3363	99	13	the	the	DET
ejpam-3363	99	14	proofs	proof	NOUN
ejpam-3363	99	15	of	of	ADP
ejpam-3363	99	16	the	the	DET
ejpam-3363	99	17	following	follow	VERB
ejpam-3363	99	18	two	two	NUM
ejpam-3363	99	19	lemmas	lemma	NOUN
ejpam-3363	99	20	.	.	PUNCT
ejpam-3363	100	1	denote	denote	VERB
ejpam-3363	100	2	by	by	ADP
ejpam-3363	100	3	j	j	PROPN
ejpam-3363	100	4	,	,	PUNCT
ejpam-3363	100	5	the	the	DET
ejpam-3363	100	6	collection	collection	NOUN
ejpam-3363	100	7	of	of	ADP
ejpam-3363	100	8	all	all	DET
ejpam-3363	100	9	closed	closed	ADJ
ejpam-3363	100	10	intervals	interval	NOUN
ejpam-3363	100	11	[	[	X
ejpam-3363	100	12	u	u	NOUN
ejpam-3363	100	13	,	,	PUNCT
ejpam-3363	100	14	v	v	ADP
ejpam-3363	100	15	]	]	X
ejpam-3363	100	16	⊂	⊂	PROPN
ejpam-3363	101	1	[	[	X
ejpam-3363	101	2	0	0	NUM
ejpam-3363	101	3	,	,	PUNCT
ejpam-3363	101	4	t	t	X
ejpam-3363	101	5	]	]	PUNCT
ejpam-3363	101	6	.	.	PUNCT
ejpam-3363	102	1	j.d	j.d	PROPN
ejpam-3363	102	2	.	.	PROPN
ejpam-3363	102	3	cagubcob	cagubcob	PROPN
ejpam-3363	102	4	,	,	PUNCT
ejpam-3363	102	5	m.	m.	NOUN
ejpam-3363	102	6	labendia	labendia	PROPN
ejpam-3363	102	7	/	/	SYM
ejpam-3363	102	8	eur	eur	PROPN
ejpam-3363	102	9	.	.	PUNCT
ejpam-3363	103	1	j.	j.	PROPN
ejpam-3363	103	2	pure	pure	PROPN
ejpam-3363	103	3	appl	appl	PROPN
ejpam-3363	103	4	.	.	PROPN
ejpam-3363	103	5	math	math	PROPN
ejpam-3363	103	6	,	,	PUNCT
ejpam-3363	103	7	12	12	NUM
ejpam-3363	103	8	(	(	PUNCT
ejpam-3363	103	9	1	1	NUM
ejpam-3363	103	10	)	)	PUNCT
ejpam-3363	103	11	(	(	PUNCT
ejpam-3363	103	12	2019	2019	NUM
ejpam-3363	103	13	)	)	PUNCT
ejpam-3363	103	14	,	,	PUNCT
ejpam-3363	103	15	101	101	NUM
ejpam-3363	103	16	-	-	SYM
ejpam-3363	103	17	117	117	NUM
ejpam-3363	103	18	105	105	NUM
ejpam-3363	103	19	lemma	lemma	PROPN
ejpam-3363	103	20	1	1	NUM
ejpam-3363	103	21	.	.	PUNCT
ejpam-3363	104	1	let	let	VERB
ejpam-3363	104	2	f	f	NOUN
ejpam-3363	104	3	:	:	PUNCT
ejpam-3363	105	1	[	[	X
ejpam-3363	105	2	0	0	NUM
ejpam-3363	105	3	,	,	PUNCT
ejpam-3363	105	4	t	t	X
ejpam-3363	105	5	]	]	PUNCT
ejpam-3363	105	6	×	×	PROPN
ejpam-3363	105	7	ω	ω	PROPN
ejpam-3363	105	8	→	→	SYM
ejpam-3363	105	9	l(u	l(u	PROPN
ejpam-3363	105	10	,	,	PUNCT
ejpam-3363	105	11	v	v	NOUN
ejpam-3363	105	12	)	)	PUNCT
ejpam-3363	105	13	be	be	AUX
ejpam-3363	105	14	an	an	DET
ejpam-3363	105	15	adapted	adapt	VERB
ejpam-3363	105	16	process	process	NOUN
ejpam-3363	105	17	and	and	CCONJ
ejpam-3363	105	18	{	{	PUNCT
ejpam-3363	105	19	(	(	PUNCT
ejpam-3363	105	20	[	[	X
ejpam-3363	105	21	ui	ui	NOUN
ejpam-3363	105	22	,	,	PUNCT
ejpam-3363	105	23	vi	vi	PROPN
ejpam-3363	105	24	]	]	PUNCT
ejpam-3363	105	25	,	,	PUNCT
ejpam-3363	105	26	ξi)}ni=1	ξi)}ni=1	PROPN
ejpam-3363	105	27	be	be	VERB
ejpam-3363	105	28	a	a	DET
ejpam-3363	105	29	finite	finite	ADJ
ejpam-3363	105	30	collection	collection	NOUN
ejpam-3363	105	31	such	such	ADJ
ejpam-3363	105	32	that	that	SCONJ
ejpam-3363	105	33	{	{	PUNCT
ejpam-3363	105	34	[	[	X
ejpam-3363	105	35	ui	ui	NOUN
ejpam-3363	105	36	,	,	PUNCT
ejpam-3363	105	37	vi	vi	PROPN
ejpam-3363	105	38	]	]	PUNCT
ejpam-3363	105	39	}	}	PUNCT
ejpam-3363	105	40	is	be	AUX
ejpam-3363	105	41	a	a	DET
ejpam-3363	105	42	collection	collection	NOUN
ejpam-3363	105	43	of	of	ADP
ejpam-3363	105	44	non	non	ADJ
ejpam-3363	105	45	-	-	ADJ
ejpam-3363	105	46	overlapping	overlapping	ADJ
ejpam-3363	105	47	intervals	interval	NOUN
ejpam-3363	105	48	in	in	ADP
ejpam-3363	105	49	j	j	PROPN
ejpam-3363	105	50	,	,	PUNCT
ejpam-3363	105	51	ξ1	ξ1	PROPN
ejpam-3363	105	52	<	<	X
ejpam-3363	105	53	ξ2	ξ2	NOUN
ejpam-3363	105	54	<	<	X
ejpam-3363	105	55	·	·	PUNCT
ejpam-3363	105	56	·	·	PUNCT
ejpam-3363	105	57	·	·	PUNCT
ejpam-3363	106	1	<	<	X
ejpam-3363	106	2	ξn	ξn	PROPN
ejpam-3363	106	3	,	,	PUNCT
ejpam-3363	106	4	and	and	CCONJ
ejpam-3363	106	5	ξi	ξi	NUM
ejpam-3363	106	6	≤	≤	NUM
ejpam-3363	106	7	ui	ui	NOUN
ejpam-3363	106	8	for	for	ADP
ejpam-3363	106	9	each	each	DET
ejpam-3363	106	10	i	i	NOUN
ejpam-3363	106	11	=	=	NOUN
ejpam-3363	106	12	1	1	NUM
ejpam-3363	106	13	,	,	PUNCT
ejpam-3363	106	14	2	2	NUM
ejpam-3363	106	15	,	,	PUNCT
ejpam-3363	106	16	.	.	PUNCT
ejpam-3363	106	17	.	.	PUNCT
ejpam-3363	106	18	.	.	PUNCT
ejpam-3363	107	1	,	,	PUNCT
ejpam-3363	107	2	n.	n.	NOUN
ejpam-3363	107	3	then	then	ADV
ejpam-3363	107	4	e	e	X
ejpam-3363	107	5	∑	∑	NOUN
ejpam-3363	107	6	i	i	PROPN
ejpam-3363	107	7	<	<	X
ejpam-3363	107	8	j	j	PROPN
ejpam-3363	107	9	〈	〈	PROPN
ejpam-3363	107	10	fξi(wvi	fξi(wvi	NOUN
ejpam-3363	107	11	−wui	−wui	X
ejpam-3363	107	12	)	)	PUNCT
ejpam-3363	107	13	,	,	PUNCT
ejpam-3363	107	14	fξj	fξj	NOUN
ejpam-3363	107	15	(	(	PUNCT
ejpam-3363	107	16	wvj	wvj	NOUN
ejpam-3363	107	17	−wuj	−wuj	NUM
ejpam-3363	107	18	)	)	PUNCT
ejpam-3363	107	19	〉	〉	NOUN
ejpam-3363	107	20	v	v	ADP
ejpam-3363	107	21			NOUN
ejpam-3363	107	22	=	=	SYM
ejpam-3363	107	23	0	0	X
ejpam-3363	107	24	.	.	PUNCT
ejpam-3363	108	1	lemma	lemma	PROPN
ejpam-3363	108	2	2	2	X
ejpam-3363	108	3	.	.	PUNCT
ejpam-3363	109	1	let	let	VERB
ejpam-3363	109	2	f	f	NOUN
ejpam-3363	109	3	:	:	PUNCT
ejpam-3363	110	1	[	[	X
ejpam-3363	110	2	0	0	NUM
ejpam-3363	110	3	,	,	PUNCT
ejpam-3363	110	4	t	t	X
ejpam-3363	110	5	]	]	PUNCT
ejpam-3363	110	6	×	×	PROPN
ejpam-3363	110	7	ω	ω	PROPN
ejpam-3363	110	8	→	→	SYM
ejpam-3363	110	9	l(u	l(u	PROPN
ejpam-3363	110	10	,	,	PUNCT
ejpam-3363	110	11	v	v	NOUN
ejpam-3363	110	12	)	)	PUNCT
ejpam-3363	110	13	be	be	AUX
ejpam-3363	110	14	an	an	DET
ejpam-3363	110	15	adapted	adapt	VERB
ejpam-3363	110	16	process	process	NOUN
ejpam-3363	110	17	and	and	CCONJ
ejpam-3363	110	18	{	{	PUNCT
ejpam-3363	110	19	(	(	PUNCT
ejpam-3363	110	20	[	[	X
ejpam-3363	110	21	ui	ui	NOUN
ejpam-3363	110	22	,	,	PUNCT
ejpam-3363	110	23	vi	vi	PROPN
ejpam-3363	110	24	]	]	PUNCT
ejpam-3363	110	25	,	,	PUNCT
ejpam-3363	110	26	ξi)}ni=1	ξi)}ni=1	PROPN
ejpam-3363	110	27	be	be	VERB
ejpam-3363	110	28	a	a	DET
ejpam-3363	110	29	finite	finite	ADJ
ejpam-3363	110	30	collection	collection	NOUN
ejpam-3363	110	31	such	such	ADJ
ejpam-3363	110	32	that	that	SCONJ
ejpam-3363	110	33	{	{	PUNCT
ejpam-3363	110	34	(	(	PUNCT
ejpam-3363	110	35	ui	ui	PROPN
ejpam-3363	110	36	,	,	PUNCT
ejpam-3363	110	37	vi	vi	PROPN
ejpam-3363	110	38	]	]	PUNCT
ejpam-3363	110	39	}	}	PUNCT
ejpam-3363	110	40	is	be	AUX
ejpam-3363	110	41	a	a	DET
ejpam-3363	110	42	collection	collection	NOUN
ejpam-3363	110	43	of	of	ADP
ejpam-3363	110	44	non	non	ADJ
ejpam-3363	110	45	-	-	ADJ
ejpam-3363	110	46	overlapping	overlapping	ADJ
ejpam-3363	110	47	intervals	interval	NOUN
ejpam-3363	110	48	in	in	ADP
ejpam-3363	110	49	j	j	PROPN
ejpam-3363	110	50	,	,	PUNCT
ejpam-3363	110	51	ξ1	ξ1	PROPN
ejpam-3363	110	52	<	<	X
ejpam-3363	110	53	ξ2	ξ2	NOUN
ejpam-3363	110	54	<	<	X
ejpam-3363	110	55	·	·	PUNCT
ejpam-3363	110	56	·	·	PUNCT
ejpam-3363	110	57	·	·	PUNCT
ejpam-3363	111	1	<	<	X
ejpam-3363	111	2	ξn	ξn	PROPN
ejpam-3363	111	3	,	,	PUNCT
ejpam-3363	111	4	and	and	CCONJ
ejpam-3363	111	5	ξi	ξi	NUM
ejpam-3363	111	6	≤	≤	NUM
ejpam-3363	111	7	ui	ui	NOUN
ejpam-3363	111	8	for	for	ADP
ejpam-3363	111	9	each	each	DET
ejpam-3363	111	10	i	i	NOUN
ejpam-3363	111	11	=	=	NOUN
ejpam-3363	111	12	1	1	NUM
ejpam-3363	111	13	,	,	PUNCT
ejpam-3363	111	14	2	2	NUM
ejpam-3363	111	15	,	,	PUNCT
ejpam-3363	111	16	.	.	PUNCT
ejpam-3363	111	17	.	.	PUNCT
ejpam-3363	111	18	.	.	PUNCT
ejpam-3363	112	1	,	,	PUNCT
ejpam-3363	112	2	n.	n.	NOUN
ejpam-3363	112	3	then	then	ADV
ejpam-3363	112	4	e	e	PROPN
ejpam-3363	112	5	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-3363	112	6	n∑	n∑	PROPN
ejpam-3363	112	7	i=1	i=1	PROPN
ejpam-3363	112	8	fξi(wvi	fξi(wvi	NOUN
ejpam-3363	112	9	−wui	−wui	X
ejpam-3363	112	10	)	)	PUNCT
ejpam-3363	113	1	∥∥∥∥∥	∥∥∥∥∥	VERB
ejpam-3363	113	2	2	2	NUM
ejpam-3363	113	3	v	v	NOUN
ejpam-3363	113	4			NOUN
ejpam-3363	113	5	=	=	PUNCT
ejpam-3363	114	1	n∑	n∑	NOUN
ejpam-3363	114	2	i=1	i=1	PROPN
ejpam-3363	115	1	e	e	X
ejpam-3363	115	2	[	[	PUNCT
ejpam-3363	115	3	‖fξi(wvi	‖fξi(wvi	X
ejpam-3363	115	4	−wui)‖	−wui)‖	PROPN
ejpam-3363	115	5	2	2	NUM
ejpam-3363	115	6	v	v	NOUN
ejpam-3363	115	7	]	]	PUNCT
ejpam-3363	116	1	=	=	PUNCT
ejpam-3363	116	2	n∑	n∑	NOUN
ejpam-3363	116	3	i=1	i=1	PROPN
ejpam-3363	117	1	(	(	PUNCT
ejpam-3363	117	2	vi	vi	PROPN
ejpam-3363	117	3	−	−	PROPN
ejpam-3363	117	4	ui)e	ui)e	PROPN
ejpam-3363	117	5	[	[	PUNCT
ejpam-3363	117	6	‖fξi‖	‖fξi‖	PROPN
ejpam-3363	117	7	2	2	NUM
ejpam-3363	117	8	l2(uq	l2(uq	PROPN
ejpam-3363	117	9	,	,	PUNCT
ejpam-3363	117	10	v	v	NOUN
ejpam-3363	117	11	)	)	PUNCT
ejpam-3363	117	12	]	]	PUNCT
ejpam-3363	117	13	.	.	PUNCT
ejpam-3363	118	1	refer	refer	VERB
ejpam-3363	118	2	to	to	ADP
ejpam-3363	118	3	[	[	X
ejpam-3363	118	4	6	6	NUM
ejpam-3363	118	5	,	,	PUNCT
ejpam-3363	118	6	example	example	NOUN
ejpam-3363	118	7	3.7	3.7	NUM
ejpam-3363	118	8	]	]	PUNCT
ejpam-3363	118	9	for	for	ADP
ejpam-3363	118	10	the	the	DET
ejpam-3363	118	11	proof	proof	NOUN
ejpam-3363	118	12	of	of	ADP
ejpam-3363	118	13	the	the	DET
ejpam-3363	118	14	following	follow	VERB
ejpam-3363	118	15	example	example	NOUN
ejpam-3363	118	16	.	.	PUNCT
ejpam-3363	119	1	example	example	NOUN
ejpam-3363	120	1	1	1	NUM
ejpam-3363	120	2	.	.	PUNCT
ejpam-3363	120	3	let	let	VERB
ejpam-3363	120	4	g	g	NOUN
ejpam-3363	120	5	:	:	PUNCT
ejpam-3363	120	6	ω	ω	PROPN
ejpam-3363	120	7	→	→	SYM
ejpam-3363	120	8	l(u	l(u	PROPN
ejpam-3363	120	9	,	,	PUNCT
ejpam-3363	120	10	v	v	NOUN
ejpam-3363	120	11	)	)	PUNCT
ejpam-3363	120	12	be	be	AUX
ejpam-3363	120	13	a	a	DET
ejpam-3363	120	14	random	random	ADJ
ejpam-3363	120	15	variable	variable	NOUN
ejpam-3363	120	16	bounded	bound	VERB
ejpam-3363	120	17	in	in	ADP
ejpam-3363	120	18	l2(uq	l2(uq	PROPN
ejpam-3363	120	19	,	,	PUNCT
ejpam-3363	120	20	v	v	NOUN
ejpam-3363	120	21	)	)	PUNCT
ejpam-3363	120	22	,	,	PUNCT
ejpam-3363	120	23	that	that	ADV
ejpam-3363	120	24	is	is	ADV
ejpam-3363	120	25	,	,	PUNCT
ejpam-3363	120	26	there	there	PRON
ejpam-3363	120	27	exists	exist	VERB
ejpam-3363	120	28	m	m	VERB
ejpam-3363	120	29	>	>	X
ejpam-3363	120	30	0	0	NUM
ejpam-3363	121	1	such	such	ADJ
ejpam-3363	121	2	that	that	SCONJ
ejpam-3363	121	3	‖g(ω)‖l2(uq	‖g(ω)‖l2(uq	NOUN
ejpam-3363	121	4	,	,	PUNCT
ejpam-3363	121	5	v	v	NOUN
ejpam-3363	121	6	)	)	PUNCT
ejpam-3363	121	7	≤	≤	NUM
ejpam-3363	121	8	m	m	VERB
ejpam-3363	121	9	for	for	ADP
ejpam-3363	121	10	all	all	DET
ejpam-3363	121	11	ω	ω	NUM
ejpam-3363	121	12	∈	∈	PROPN
ejpam-3363	121	13	ω	ω	NOUN
ejpam-3363	121	14	and	and	CCONJ
ejpam-3363	121	15	let	let	VERB
ejpam-3363	121	16	0̂	0̂	PROPN
ejpam-3363	121	17	:	:	PUNCT
ejpam-3363	122	1	ω	ω	X
ejpam-3363	122	2	→	→	SYM
ejpam-3363	122	3	l(u	l(u	PROPN
ejpam-3363	122	4	,	,	PUNCT
ejpam-3363	122	5	v	v	NOUN
ejpam-3363	122	6	)	)	PUNCT
ejpam-3363	122	7	be	be	AUX
ejpam-3363	122	8	a	a	DET
ejpam-3363	122	9	random	random	ADJ
ejpam-3363	122	10	variable	variable	NOUN
ejpam-3363	122	11	such	such	ADJ
ejpam-3363	122	12	that	that	PRON
ejpam-3363	122	13	for	for	ADP
ejpam-3363	122	14	all	all	DET
ejpam-3363	122	15	ω	ω	PROPN
ejpam-3363	122	16	∈	∈	PROPN
ejpam-3363	122	17	ω	ω	PROPN
ejpam-3363	122	18	,	,	PUNCT
ejpam-3363	122	19	0̂(ω	0̂(ω	PROPN
ejpam-3363	122	20	)	)	PUNCT
ejpam-3363	122	21	is	be	AUX
ejpam-3363	122	22	the	the	DET
ejpam-3363	122	23	zero	zero	NUM
ejpam-3363	122	24	operator	operator	NOUN
ejpam-3363	122	25	in	in	ADP
ejpam-3363	122	26	l(u	l(u	PROPN
ejpam-3363	122	27	,	,	PUNCT
ejpam-3363	122	28	v	v	NOUN
ejpam-3363	122	29	)	)	PUNCT
ejpam-3363	122	30	.	.	PUNCT
ejpam-3363	123	1	let	let	VERB
ejpam-3363	123	2	s	s	PRON
ejpam-3363	123	3	∈	∈	NOUN
ejpam-3363	123	4	[	[	X
ejpam-3363	123	5	0	0	NUM
ejpam-3363	123	6	,	,	PUNCT
ejpam-3363	123	7	t	t	PROPN
ejpam-3363	123	8	]	]	PUNCT
ejpam-3363	123	9	be	be	AUX
ejpam-3363	123	10	fixed	fix	VERB
ejpam-3363	123	11	.	.	PUNCT
ejpam-3363	124	1	let	let	VERB
ejpam-3363	124	2	f	f	NOUN
ejpam-3363	124	3	:	:	PUNCT
ejpam-3363	125	1	[	[	X
ejpam-3363	125	2	0	0	NUM
ejpam-3363	125	3	,	,	PUNCT
ejpam-3363	125	4	t	t	X
ejpam-3363	125	5	]	]	PUNCT
ejpam-3363	125	6	×	×	PROPN
ejpam-3363	125	7	ω	ω	PROPN
ejpam-3363	125	8	→	→	SYM
ejpam-3363	125	9	l(u	l(u	PROPN
ejpam-3363	125	10	,	,	PUNCT
ejpam-3363	125	11	v	v	NOUN
ejpam-3363	125	12	)	)	PUNCT
ejpam-3363	125	13	be	be	AUX
ejpam-3363	125	14	an	an	DET
ejpam-3363	125	15	adapted	adapt	VERB
ejpam-3363	125	16	process	process	NOUN
ejpam-3363	125	17	on	on	ADP
ejpam-3363	125	18	a	a	DET
ejpam-3363	125	19	filtered	filter	VERB
ejpam-3363	125	20	probability	probability	NOUN
ejpam-3363	125	21	space	space	NOUN
ejpam-3363	125	22	(	(	PUNCT
ejpam-3363	125	23	ω	ω	PROPN
ejpam-3363	125	24	,	,	PUNCT
ejpam-3363	125	25	f	f	PROPN
ejpam-3363	125	26	,	,	PUNCT
ejpam-3363	125	27	{	{	PUNCT
ejpam-3363	125	28	ft},p	ft},p	NOUN
ejpam-3363	125	29	)	)	PUNCT
ejpam-3363	125	30	such	such	ADJ
ejpam-3363	125	31	that	that	PRON
ejpam-3363	125	32	for	for	ADP
ejpam-3363	125	33	t	t	PROPN
ejpam-3363	125	34	∈	∈	PROPN
ejpam-3363	126	1	[	[	X
ejpam-3363	126	2	0	0	NUM
ejpam-3363	126	3	,	,	PUNCT
ejpam-3363	126	4	t	t	X
ejpam-3363	126	5	]	]	PUNCT
ejpam-3363	126	6	,	,	PUNCT
ejpam-3363	126	7	ft	ft	PROPN
ejpam-3363	126	8	=	=	PUNCT
ejpam-3363	126	9	{	{	PUNCT
ejpam-3363	126	10	g	g	NOUN
ejpam-3363	126	11	if	if	SCONJ
ejpam-3363	126	12	t	t	PROPN
ejpam-3363	126	13	=	=	SYM
ejpam-3363	126	14	s	s	PART
ejpam-3363	126	15	0̂	0̂	PROPN
ejpam-3363	126	16	if	if	SCONJ
ejpam-3363	126	17	t	t	PROPN
ejpam-3363	126	18	6=	6=	PROPN
ejpam-3363	126	19	s.	s.	PROPN
ejpam-3363	127	1	then	then	ADV
ejpam-3363	127	2	f	f	PROPN
ejpam-3363	127	3	is	be	AUX
ejpam-3363	127	4	im	im	NOUN
ejpam-3363	127	5	-	-	PUNCT
ejpam-3363	127	6	integrable	integrable	ADJ
ejpam-3363	127	7	to	to	ADP
ejpam-3363	127	8	the	the	DET
ejpam-3363	127	9	zero	zero	NUM
ejpam-3363	127	10	random	random	ADJ
ejpam-3363	127	11	variable	variable	NOUN
ejpam-3363	127	12	0	0	NUM
ejpam-3363	127	13	∈	∈	PROPN
ejpam-3363	127	14	l2(ω	l2(ω	PROPN
ejpam-3363	127	15	,	,	PUNCT
ejpam-3363	127	16	v	v	NOUN
ejpam-3363	127	17	)	)	PUNCT
ejpam-3363	127	18	on	on	ADP
ejpam-3363	127	19	[	[	X
ejpam-3363	127	20	0	0	NUM
ejpam-3363	127	21	,	,	PUNCT
ejpam-3363	127	22	t	t	X
ejpam-3363	127	23	]	]	PUNCT
ejpam-3363	127	24	.	.	PUNCT
ejpam-3363	128	1	in	in	ADP
ejpam-3363	128	2	the	the	DET
ejpam-3363	128	3	following	follow	VERB
ejpam-3363	128	4	proofs	proof	NOUN
ejpam-3363	128	5	,	,	PUNCT
ejpam-3363	128	6	denote	denote	VERB
ejpam-3363	128	7	by	by	ADP
ejpam-3363	128	8	leb∗	leb∗	PROPN
ejpam-3363	128	9	and	and	CCONJ
ejpam-3363	128	10	leb	leb	PROPN
ejpam-3363	128	11	,	,	PUNCT
ejpam-3363	128	12	the	the	DET
ejpam-3363	128	13	lebesgue	lebesgue	ADJ
ejpam-3363	128	14	outer	outer	ADJ
ejpam-3363	128	15	measure	measure	NOUN
ejpam-3363	128	16	and	and	CCONJ
ejpam-3363	128	17	lebesgue	lebesgue	NOUN
ejpam-3363	128	18	measure	measure	NOUN
ejpam-3363	128	19	,	,	PUNCT
ejpam-3363	128	20	respectively	respectively	ADV
ejpam-3363	128	21	.	.	PUNCT
ejpam-3363	128	22	example	example	NOUN
ejpam-3363	128	23	2	2	NUM
ejpam-3363	128	24	.	.	PUNCT
ejpam-3363	129	1	let	let	VERB
ejpam-3363	129	2	f	f	NOUN
ejpam-3363	129	3	:	:	PUNCT
ejpam-3363	130	1	[	[	X
ejpam-3363	130	2	0	0	NUM
ejpam-3363	130	3	,	,	PUNCT
ejpam-3363	130	4	t	t	X
ejpam-3363	130	5	]	]	PUNCT
ejpam-3363	130	6	×ω→	×ω→	PROPN
ejpam-3363	130	7	l(u	l(u	PROPN
ejpam-3363	130	8	,	,	PUNCT
ejpam-3363	130	9	v	v	NOUN
ejpam-3363	130	10	)	)	PUNCT
ejpam-3363	130	11	be	be	AUX
ejpam-3363	130	12	an	an	DET
ejpam-3363	130	13	adapted	adapt	VERB
ejpam-3363	130	14	process	process	NOUN
ejpam-3363	130	15	such	such	ADJ
ejpam-3363	130	16	that	that	SCONJ
ejpam-3363	130	17	e	e	NOUN
ejpam-3363	130	18	[	[	PUNCT
ejpam-3363	130	19	‖ft‖2l2(uq	‖ft‖2l2(uq	NUM
ejpam-3363	130	20	,	,	PUNCT
ejpam-3363	130	21	v	v	NOUN
ejpam-3363	130	22	)	)	PUNCT
ejpam-3363	130	23	]	]	PUNCT
ejpam-3363	131	1	=	=	PUNCT
ejpam-3363	131	2	0	0	PUNCT
ejpam-3363	131	3	almost	almost	ADV
ejpam-3363	131	4	everywhere	everywhere	ADV
ejpam-3363	131	5	(	(	PUNCT
ejpam-3363	131	6	abbrev	abbrev	NOUN
ejpam-3363	131	7	.	.	PUNCT
ejpam-3363	132	1	as	as	ADP
ejpam-3363	132	2	a.e	a.e	PROPN
ejpam-3363	132	3	.	.	PUNCT
ejpam-3363	132	4	)	)	PUNCT
ejpam-3363	133	1	on	on	ADP
ejpam-3363	133	2	[	[	X
ejpam-3363	133	3	0	0	NUM
ejpam-3363	133	4	,	,	PUNCT
ejpam-3363	133	5	t	t	X
ejpam-3363	133	6	]	]	PUNCT
ejpam-3363	133	7	.	.	PUNCT
ejpam-3363	134	1	then	then	ADV
ejpam-3363	134	2	f	f	PROPN
ejpam-3363	134	3	is	be	AUX
ejpam-3363	134	4	im	im	NOUN
ejpam-3363	134	5	-	-	PUNCT
ejpam-3363	134	6	integrable	integrable	ADJ
ejpam-3363	134	7	to	to	ADP
ejpam-3363	134	8	0	0	NUM
ejpam-3363	134	9	on	on	ADP
ejpam-3363	134	10	[	[	X
ejpam-3363	134	11	0	0	NUM
ejpam-3363	134	12	,	,	PUNCT
ejpam-3363	134	13	t	t	X
ejpam-3363	134	14	]	]	PUNCT
ejpam-3363	134	15	.	.	PUNCT
ejpam-3363	135	1	proof	proof	NOUN
ejpam-3363	135	2	.	.	PUNCT
ejpam-3363	136	1	let	let	VERB
ejpam-3363	136	2	ε	ε	PROPN
ejpam-3363	136	3	>	>	X
ejpam-3363	136	4	0	0	PUNCT
ejpam-3363	136	5	be	be	AUX
ejpam-3363	136	6	given	give	VERB
ejpam-3363	136	7	.	.	PUNCT
ejpam-3363	137	1	let	let	VERB
ejpam-3363	137	2	g	g	NOUN
ejpam-3363	137	3	=	=	PRON
ejpam-3363	137	4	{	{	PUNCT
ejpam-3363	137	5	t	t	NOUN
ejpam-3363	137	6	∈	∈	PROPN
ejpam-3363	138	1	[	[	X
ejpam-3363	138	2	0	0	NUM
ejpam-3363	138	3	,	,	PUNCT
ejpam-3363	138	4	t	t	X
ejpam-3363	138	5	]	]	PUNCT
ejpam-3363	138	6	:	:	PUNCT
ejpam-3363	138	7	e	e	X
ejpam-3363	138	8	[	[	PUNCT
ejpam-3363	138	9	‖ft‖l2(uq	‖ft‖l2(uq	NOUN
ejpam-3363	138	10	,	,	PUNCT
ejpam-3363	138	11	v	v	NOUN
ejpam-3363	138	12	)	)	PUNCT
ejpam-3363	138	13	2	2	NUM
ejpam-3363	138	14	]	]	PUNCT
ejpam-3363	138	15	6=	6=	ADP
ejpam-3363	138	16	0	0	NUM
ejpam-3363	138	17	}	}	PUNCT
ejpam-3363	138	18	.	.	PUNCT
ejpam-3363	139	1	then	then	ADV
ejpam-3363	139	2	,	,	PUNCT
ejpam-3363	139	3	leb(g	leb(g	PROPN
ejpam-3363	139	4	)	)	PUNCT
ejpam-3363	139	5	=	=	SYM
ejpam-3363	139	6	0	0	NUM
ejpam-3363	140	1	and	and	CCONJ
ejpam-3363	140	2	so	so	ADV
ejpam-3363	140	3	g	g	PROPN
ejpam-3363	140	4	is	be	AUX
ejpam-3363	140	5	measurable	measurable	ADJ
ejpam-3363	140	6	.	.	PUNCT
ejpam-3363	141	1	let	let	VERB
ejpam-3363	141	2	ξ	ξ	PROPN
ejpam-3363	141	3	∈	∈	PROPN
ejpam-3363	141	4	g.	g.	NOUN
ejpam-3363	141	5	for	for	ADP
ejpam-3363	141	6	any	any	DET
ejpam-3363	141	7	[	[	X
ejpam-3363	141	8	u	u	NOUN
ejpam-3363	141	9	,	,	PUNCT
ejpam-3363	141	10	v	v	ADP
ejpam-3363	141	11	]	]	X
ejpam-3363	141	12	⊂	⊂	X
ejpam-3363	142	1	[	[	X
ejpam-3363	142	2	ξ	ξ	PROPN
ejpam-3363	142	3	,	,	PUNCT
ejpam-3363	142	4	t	t	X
ejpam-3363	142	5	]	]	PUNCT
ejpam-3363	142	6	,	,	PUNCT
ejpam-3363	142	7	e	e	X
ejpam-3363	142	8	[	[	PUNCT
ejpam-3363	142	9	‖fξ(wv	‖fξ(wv	NOUN
ejpam-3363	142	10	−wu)‖2v	−wu)‖2v	NOUN
ejpam-3363	142	11	]	]	X
ejpam-3363	142	12	=	=	PUNCT
ejpam-3363	142	13	(	(	PUNCT
ejpam-3363	142	14	v	v	NOUN
ejpam-3363	142	15	−	−	NOUN
ejpam-3363	142	16	u)e	u)e	ADJ
ejpam-3363	142	17	[	[	PUNCT
ejpam-3363	142	18	‖fξ‖2l2(uq	‖fξ‖2l2(uq	NUM
ejpam-3363	142	19	,	,	PUNCT
ejpam-3363	142	20	v	v	NOUN
ejpam-3363	142	21	)	)	PUNCT
ejpam-3363	142	22	]	]	PUNCT
ejpam-3363	142	23	.	.	PUNCT
ejpam-3363	143	1	j.d	j.d	PROPN
ejpam-3363	143	2	.	.	PROPN
ejpam-3363	143	3	cagubcob	cagubcob	PROPN
ejpam-3363	143	4	,	,	PUNCT
ejpam-3363	143	5	m.	m.	NOUN
ejpam-3363	143	6	labendia	labendia	PROPN
ejpam-3363	143	7	/	/	SYM
ejpam-3363	143	8	eur	eur	PROPN
ejpam-3363	143	9	.	.	PUNCT
ejpam-3363	144	1	j.	j.	PROPN
ejpam-3363	144	2	pure	pure	PROPN
ejpam-3363	144	3	appl	appl	PROPN
ejpam-3363	144	4	.	.	PROPN
ejpam-3363	144	5	math	math	PROPN
ejpam-3363	144	6	,	,	PUNCT
ejpam-3363	144	7	12	12	NUM
ejpam-3363	144	8	(	(	PUNCT
ejpam-3363	144	9	1	1	NUM
ejpam-3363	144	10	)	)	PUNCT
ejpam-3363	144	11	(	(	PUNCT
ejpam-3363	144	12	2019	2019	NUM
ejpam-3363	144	13	)	)	PUNCT
ejpam-3363	144	14	,	,	PUNCT
ejpam-3363	144	15	101	101	NUM
ejpam-3363	144	16	-	-	SYM
ejpam-3363	144	17	117	117	NUM
ejpam-3363	144	18	106	106	NUM
ejpam-3363	144	19	let	let	VERB
ejpam-3363	144	20	am	be	AUX
ejpam-3363	144	21	=	=	PUNCT
ejpam-3363	144	22	m∑	m∑	ADV
ejpam-3363	144	23	k=1	k=1	PROPN
ejpam-3363	145	1	〈	〈	PROPN
ejpam-3363	145	2	fξ(wv	fξ(wv	NOUN
ejpam-3363	145	3	−wu	−wu	NUM
ejpam-3363	145	4	)	)	PUNCT
ejpam-3363	145	5	,	,	PUNCT
ejpam-3363	145	6	gk〉2	gk〉2	PROPN
ejpam-3363	145	7	,	,	PUNCT
ejpam-3363	145	8	where	where	SCONJ
ejpam-3363	145	9	{	{	PUNCT
ejpam-3363	145	10	gk	gk	NOUN
ejpam-3363	145	11	}	}	PUNCT
ejpam-3363	145	12	is	be	AUX
ejpam-3363	145	13	an	an	DET
ejpam-3363	145	14	onb	onb	ADJ
ejpam-3363	145	15	in	in	ADP
ejpam-3363	145	16	v	v	NOUN
ejpam-3363	145	17	.	.	PUNCT
ejpam-3363	146	1	since	since	SCONJ
ejpam-3363	146	2	am	am	VERB
ejpam-3363	146	3	→	→	SYM
ejpam-3363	146	4	g	g	NOUN
ejpam-3363	146	5	:	:	PUNCT
ejpam-3363	146	6	=	=	SYM
ejpam-3363	146	7	∞∑	∞∑	NUM
ejpam-3363	146	8	k=1	k=1	PUNCT
ejpam-3363	146	9	〈	〈	PROPN
ejpam-3363	146	10	fξ(wv	fξ(wv	NOUN
ejpam-3363	146	11	−wu	−wu	NUM
ejpam-3363	146	12	)	)	PUNCT
ejpam-3363	146	13	,	,	PUNCT
ejpam-3363	146	14	gk〉2	gk〉2	PROPN
ejpam-3363	146	15	asm→∞	asm→∞	NOUN
ejpam-3363	146	16	andam	andam	PROPN
ejpam-3363	146	17	≤	≤	PROPN
ejpam-3363	146	18	am+1	am+1	PROPN
ejpam-3363	146	19	,	,	PUNCT
ejpam-3363	146	20	by	by	ADP
ejpam-3363	146	21	the	the	DET
ejpam-3363	146	22	monotone	monotone	ADJ
ejpam-3363	146	23	convergence	convergence	NOUN
ejpam-3363	146	24	theorem	theorem	VERB
ejpam-3363	146	25	for	for	ADP
ejpam-3363	146	26	lebesgue	lebesgue	PROPN
ejpam-3363	146	27	integral	integral	ADJ
ejpam-3363	146	28	,	,	PUNCT
ejpam-3363	146	29	lim	lim	PROPN
ejpam-3363	146	30	m→∞	m→∞	NUM
ejpam-3363	146	31	e	e	NOUN
ejpam-3363	146	32	[	[	PUNCT
ejpam-3363	146	33	m∑	m∑	ADP
ejpam-3363	146	34	k=1	k=1	PROPN
ejpam-3363	146	35	〈	〈	PROPN
ejpam-3363	146	36	fξ(wv	fξ(wv	NOUN
ejpam-3363	146	37	−wu	−wu	NUM
ejpam-3363	146	38	)	)	PUNCT
ejpam-3363	146	39	,	,	PUNCT
ejpam-3363	146	40	gk〉2	gk〉2	PROPN
ejpam-3363	146	41	]	]	PUNCT
ejpam-3363	147	1	=	=	PUNCT
ejpam-3363	147	2	e	e	X
ejpam-3363	147	3	[	[	PUNCT
ejpam-3363	147	4	∞∑	∞∑	NUM
ejpam-3363	147	5	k=1	k=1	ADP
ejpam-3363	147	6	〈	〈	PROPN
ejpam-3363	147	7	fξ(wv	fξ(wv	NOUN
ejpam-3363	147	8	−wu	−wu	NUM
ejpam-3363	147	9	)	)	PUNCT
ejpam-3363	147	10	,	,	PUNCT
ejpam-3363	147	11	gk〉2	gk〉2	PROPN
ejpam-3363	147	12	]	]	PUNCT
ejpam-3363	147	13	=	=	PUNCT
ejpam-3363	147	14	e	e	X
ejpam-3363	147	15	[	[	PUNCT
ejpam-3363	147	16	‖fξ(wv	‖fξ(wv	NOUN
ejpam-3363	147	17	−wu)‖2v	−wu)‖2v	NOUN
ejpam-3363	147	18	]	]	X
ejpam-3363	147	19	<	<	X
ejpam-3363	147	20	∞.	∞.	PROPN
ejpam-3363	147	21	(	(	PUNCT
ejpam-3363	147	22	3	3	NUM
ejpam-3363	147	23	)	)	PUNCT
ejpam-3363	147	24	thus	thus	ADV
ejpam-3363	147	25	,	,	PUNCT
ejpam-3363	147	26	there	there	PRON
ejpam-3363	147	27	exists	exist	VERB
ejpam-3363	147	28	n	n	PRON
ejpam-3363	147	29	∈	∈	PROPN
ejpam-3363	147	30	n	n	PRON
ejpam-3363	147	31	such	such	ADJ
ejpam-3363	147	32	that	that	SCONJ
ejpam-3363	147	33	e	e	NOUN
ejpam-3363	147	34	[	[	PUNCT
ejpam-3363	147	35	‖fξ‖2l2(uq	‖fξ‖2l2(uq	NUM
ejpam-3363	147	36	,	,	PUNCT
ejpam-3363	147	37	v	v	NOUN
ejpam-3363	147	38	)	)	PUNCT
ejpam-3363	147	39	]	]	PUNCT
ejpam-3363	148	1	<	<	X
ejpam-3363	148	2	n	n	X
ejpam-3363	148	3	.	.	PUNCT
ejpam-3363	149	1	now	now	ADV
ejpam-3363	149	2	,	,	PUNCT
ejpam-3363	149	3	since	since	SCONJ
ejpam-3363	149	4	g	g	PROPN
ejpam-3363	149	5	is	be	AUX
ejpam-3363	149	6	measurable	measurable	ADJ
ejpam-3363	149	7	,	,	PUNCT
ejpam-3363	149	8	there	there	PRON
ejpam-3363	149	9	exists	exist	VERB
ejpam-3363	149	10	an	an	DET
ejpam-3363	149	11	open	open	ADJ
ejpam-3363	149	12	set	set	NOUN
ejpam-3363	149	13	o	o	NOUN
ejpam-3363	149	14	containing	contain	VERB
ejpam-3363	149	15	g	g	PRON
ejpam-3363	149	16	such	such	ADJ
ejpam-3363	149	17	that	that	SCONJ
ejpam-3363	149	18	leb(o	leb(o	PROPN
ejpam-3363	149	19	)	)	PUNCT
ejpam-3363	149	20	<	<	X
ejpam-3363	149	21	ε	ε	PROPN
ejpam-3363	149	22	2n	2n	NUM
ejpam-3363	149	23	.	.	PUNCT
ejpam-3363	150	1	thus	thus	ADV
ejpam-3363	150	2	,	,	PUNCT
ejpam-3363	150	3	for	for	ADP
ejpam-3363	150	4	all	all	DET
ejpam-3363	150	5	ξ	ξ	PROPN
ejpam-3363	150	6	∈	∈	PROPN
ejpam-3363	150	7	g	g	NOUN
ejpam-3363	150	8	,	,	PUNCT
ejpam-3363	150	9	there	there	PRON
ejpam-3363	150	10	exists	exist	VERB
ejpam-3363	150	11	δ1(ξ	δ1(ξ	PRON
ejpam-3363	150	12	)	)	PUNCT
ejpam-3363	150	13	>	>	X
ejpam-3363	150	14	0	0	NUM
ejpam-3363	151	1	such	such	ADJ
ejpam-3363	151	2	that	that	SCONJ
ejpam-3363	151	3	[	[	X
ejpam-3363	151	4	ξ	ξ	X
ejpam-3363	151	5	,	,	PUNCT
ejpam-3363	151	6	ξ	ξ	PROPN
ejpam-3363	151	7	+	+	PUNCT
ejpam-3363	151	8	δ1(ξ	δ1(ξ	NUM
ejpam-3363	151	9	)	)	PUNCT
ejpam-3363	151	10	)	)	PUNCT
ejpam-3363	152	1	⊂	⊂	PROPN
ejpam-3363	152	2	o.	o.	PROPN
ejpam-3363	152	3	let	let	VERB
ejpam-3363	152	4	d′	d′	X
ejpam-3363	152	5	=	=	PUNCT
ejpam-3363	152	6	{	{	PUNCT
ejpam-3363	152	7	(	(	PUNCT
ejpam-3363	152	8	[	[	X
ejpam-3363	152	9	u	u	NOUN
ejpam-3363	152	10	,	,	PUNCT
ejpam-3363	152	11	v	v	ADP
ejpam-3363	152	12	]	]	X
ejpam-3363	152	13	,	,	PUNCT
ejpam-3363	152	14	ξ	ξ	X
ejpam-3363	152	15	)	)	PUNCT
ejpam-3363	152	16	}	}	PUNCT
ejpam-3363	152	17	be	be	AUX
ejpam-3363	152	18	a	a	DET
ejpam-3363	152	19	δ1	δ1	NOUN
ejpam-3363	152	20	-	-	PUNCT
ejpam-3363	152	21	fine	fine	NOUN
ejpam-3363	152	22	belated	belate	VERB
ejpam-3363	152	23	mcshane	mcshane	PROPN
ejpam-3363	152	24	partial	partial	ADJ
ejpam-3363	152	25	division	division	NOUN
ejpam-3363	152	26	such	such	ADJ
ejpam-3363	152	27	that	that	SCONJ
ejpam-3363	152	28	each	each	DET
ejpam-3363	152	29	ξ	ξ	PROPN
ejpam-3363	152	30	∈	∈	PROPN
ejpam-3363	152	31	g.	g.	NOUN
ejpam-3363	152	32	then	then	ADV
ejpam-3363	152	33	,	,	PUNCT
ejpam-3363	152	34	(	(	PUNCT
ejpam-3363	152	35	d′	d′	X
ejpam-3363	152	36	)	)	PUNCT
ejpam-3363	152	37	∑	∑	PUNCT
ejpam-3363	152	38	(	(	PUNCT
ejpam-3363	152	39	v	v	ADP
ejpam-3363	152	40	−	−	PROPN
ejpam-3363	152	41	u	u	NOUN
ejpam-3363	152	42	)	)	PUNCT
ejpam-3363	152	43	<	<	X
ejpam-3363	152	44	ε	ε	PROPN
ejpam-3363	152	45	2n	2n	NUM
ejpam-3363	152	46	and	and	CCONJ
ejpam-3363	152	47	so	so	ADV
ejpam-3363	152	48	e	e	PROPN
ejpam-3363	152	49	[	[	X
ejpam-3363	152	50	∥∥∥(d′	∥∥∥(d′	PROPN
ejpam-3363	152	51	)	)	PUNCT
ejpam-3363	152	52	∑	∑	PUNCT
ejpam-3363	152	53	fξ(wv	fξ(wv	VERB
ejpam-3363	152	54	−wu)−	−wu)−	ADP
ejpam-3363	152	55	0	0	NUM
ejpam-3363	152	56	∥∥∥2	∥∥∥2	NOUN
ejpam-3363	152	57	v	v	ADP
ejpam-3363	152	58	]	]	PUNCT
ejpam-3363	152	59	≤	≤	NUM
ejpam-3363	152	60	2(d′	2(d′	NUM
ejpam-3363	152	61	)	)	PUNCT
ejpam-3363	152	62	∑	∑	PUNCT
ejpam-3363	152	63	(	(	PUNCT
ejpam-3363	152	64	v	v	NOUN
ejpam-3363	152	65	−	−	NOUN
ejpam-3363	152	66	u)e	u)e	ADJ
ejpam-3363	152	67	[	[	PUNCT
ejpam-3363	152	68	‖fξ‖2l2(uq	‖fξ‖2l2(uq	NUM
ejpam-3363	152	69	,	,	PUNCT
ejpam-3363	152	70	v	v	NOUN
ejpam-3363	152	71	)	)	PUNCT
ejpam-3363	152	72	]	]	PUNCT
ejpam-3363	152	73	<	<	X
ejpam-3363	152	74	2n	2n	NUM
ejpam-3363	152	75	·	·	PUNCT
ejpam-3363	152	76	ε	ε	PROPN
ejpam-3363	152	77	2n	2n	NUM
ejpam-3363	152	78	=	=	SYM
ejpam-3363	152	79	ε	ε	PROPN
ejpam-3363	152	80	.	.	PUNCT
ejpam-3363	153	1	(	(	PUNCT
ejpam-3363	153	2	4	4	NUM
ejpam-3363	153	3	)	)	PUNCT
ejpam-3363	153	4	thus	thus	ADV
ejpam-3363	153	5	,	,	PUNCT
ejpam-3363	153	6	for	for	SCONJ
ejpam-3363	153	7	any	any	DET
ejpam-3363	153	8	δ	δ	NOUN
ejpam-3363	153	9	-	-	PUNCT
ejpam-3363	153	10	fine	fine	NOUN
ejpam-3363	153	11	belated	belate	VERB
ejpam-3363	153	12	mcshane	mcshane	PROPN
ejpam-3363	153	13	partial	partial	ADJ
ejpam-3363	153	14	division	division	NOUN
ejpam-3363	154	1	d	d	NOUN
ejpam-3363	154	2	=	=	PRON
ejpam-3363	154	3	{	{	PUNCT
ejpam-3363	154	4	(	(	PUNCT
ejpam-3363	154	5	[	[	X
ejpam-3363	154	6	u	u	NOUN
ejpam-3363	154	7	,	,	PUNCT
ejpam-3363	154	8	v	v	ADP
ejpam-3363	154	9	]	]	X
ejpam-3363	154	10	,	,	PUNCT
ejpam-3363	154	11	ξ	ξ	X
ejpam-3363	154	12	)	)	PUNCT
ejpam-3363	154	13	}	}	PUNCT
ejpam-3363	154	14	where	where	SCONJ
ejpam-3363	154	15	δ	δ	PROPN
ejpam-3363	154	16	(	(	PUNCT
ejpam-3363	154	17	·	·	PUNCT
ejpam-3363	154	18	)	)	PUNCT
ejpam-3363	154	19	>	>	X
ejpam-3363	154	20	0	0	PUNCT
ejpam-3363	154	21	on	on	ADP
ejpam-3363	154	22	[	[	X
ejpam-3363	154	23	0	0	NUM
ejpam-3363	154	24	,	,	PUNCT
ejpam-3363	154	25	t	t	NOUN
ejpam-3363	154	26	]	]	PUNCT
ejpam-3363	154	27	and	and	CCONJ
ejpam-3363	154	28	δ(ξ	δ(ξ	NOUN
ejpam-3363	154	29	)	)	PUNCT
ejpam-3363	154	30	≥	≥	NOUN
ejpam-3363	154	31	δ1(ξ	δ1(ξ	NOUN
ejpam-3363	154	32	)	)	PUNCT
ejpam-3363	154	33	for	for	ADP
ejpam-3363	154	34	ξ	ξ	PROPN
ejpam-3363	154	35	∈	∈	PROPN
ejpam-3363	154	36	g	g	NOUN
ejpam-3363	154	37	,	,	PUNCT
ejpam-3363	154	38	we	we	PRON
ejpam-3363	154	39	have	have	VERB
ejpam-3363	154	40	e	e	NOUN
ejpam-3363	154	41	[	[	NOUN
ejpam-3363	154	42	∥∥∥(d	∥∥∥(d	PUNCT
ejpam-3363	154	43	)	)	PUNCT
ejpam-3363	154	44	∑	∑	PUNCT
ejpam-3363	154	45	fξ(wv	fξ(wv	VERB
ejpam-3363	154	46	−wu)−	−wu)−	ADP
ejpam-3363	154	47	0	0	NUM
ejpam-3363	154	48	∥∥∥2	∥∥∥2	NOUN
ejpam-3363	154	49	v	v	ADP
ejpam-3363	154	50	]	]	PUNCT
ejpam-3363	154	51	≤	≤	NUM
ejpam-3363	154	52	2(dξ∈g	2(dξ∈g	NUM
ejpam-3363	154	53	)	)	PUNCT
ejpam-3363	154	54	∑	∑	PUNCT
ejpam-3363	154	55	(	(	PUNCT
ejpam-3363	154	56	v	v	NOUN
ejpam-3363	154	57	−	−	NOUN
ejpam-3363	154	58	u)e	u)e	ADJ
ejpam-3363	154	59	[	[	PUNCT
ejpam-3363	154	60	‖fξ‖2l2(uq	‖fξ‖2l2(uq	NUM
ejpam-3363	154	61	,	,	PUNCT
ejpam-3363	154	62	v	v	NOUN
ejpam-3363	154	63	)	)	PUNCT
ejpam-3363	154	64	]	]	PUNCT
ejpam-3363	155	1	+	+	PUNCT
ejpam-3363	155	2	2(dξ∈[0,t	2(dξ∈[0,t	NUM
ejpam-3363	155	3	]	]	SYM
ejpam-3363	155	4	\g	\g	NUM
ejpam-3363	155	5	)	)	PUNCT
ejpam-3363	155	6	∑	∑	PUNCT
ejpam-3363	155	7	(	(	PUNCT
ejpam-3363	155	8	v	v	ADP
ejpam-3363	155	9	−	−	NOUN
ejpam-3363	155	10	u)e	u)e	ADJ
ejpam-3363	155	11	[	[	PUNCT
ejpam-3363	155	12	‖fξ‖2l2(uq	‖fξ‖2l2(uq	NUM
ejpam-3363	155	13	,	,	PUNCT
ejpam-3363	155	14	v	v	NOUN
ejpam-3363	155	15	)	)	PUNCT
ejpam-3363	155	16	]	]	PUNCT
ejpam-3363	156	1	<	<	X
ejpam-3363	156	2	ε	ε	PROPN
ejpam-3363	156	3	.	.	PUNCT
ejpam-3363	156	4	(	(	PUNCT
ejpam-3363	156	5	5	5	X
ejpam-3363	156	6	)	)	PUNCT
ejpam-3363	156	7	the	the	DET
ejpam-3363	156	8	above	above	ADJ
ejpam-3363	156	9	inequality	inequality	NOUN
ejpam-3363	156	10	also	also	ADV
ejpam-3363	156	11	holds	hold	VERB
ejpam-3363	156	12	for	for	ADP
ejpam-3363	156	13	(	(	PUNCT
ejpam-3363	156	14	δ	δ	PROPN
ejpam-3363	156	15	,	,	PUNCT
ejpam-3363	156	16	η)-fine	η)-fine	PROPN
ejpam-3363	156	17	belated	belate	VERB
ejpam-3363	156	18	mcshane	mcshane	PROPN
ejpam-3363	156	19	partial	partial	ADJ
ejpam-3363	156	20	division	division	NOUN
ejpam-3363	156	21	of	of	ADP
ejpam-3363	156	22	[	[	X
ejpam-3363	156	23	0	0	NUM
ejpam-3363	156	24	,	,	PUNCT
ejpam-3363	156	25	t	t	X
ejpam-3363	156	26	]	]	PUNCT
ejpam-3363	156	27	.	.	PUNCT
ejpam-3363	157	1	thus	thus	ADV
ejpam-3363	157	2	,	,	PUNCT
ejpam-3363	157	3	f	f	PROPN
ejpam-3363	157	4	is	be	AUX
ejpam-3363	157	5	im	im	ADV
ejpam-3363	157	6	-	-	PUNCT
ejpam-3363	157	7	integrable	integrable	ADJ
ejpam-3363	157	8	to	to	ADP
ejpam-3363	157	9	0	0	NUM
ejpam-3363	157	10	on	on	ADP
ejpam-3363	157	11	[	[	X
ejpam-3363	157	12	0	0	NUM
ejpam-3363	157	13	,	,	PUNCT
ejpam-3363	157	14	t	t	X
ejpam-3363	157	15	]	]	PUNCT
ejpam-3363	157	16	.	.	PUNCT
ejpam-3363	158	1	it	it	PRON
ejpam-3363	158	2	is	be	AUX
ejpam-3363	158	3	worth	worth	ADJ
ejpam-3363	158	4	noting	note	VERB
ejpam-3363	158	5	that	that	SCONJ
ejpam-3363	158	6	the	the	DET
ejpam-3363	158	7	itô-mcshane	itô-mcshane	PRON
ejpam-3363	158	8	integral	integral	ADJ
ejpam-3363	158	9	possesses	possesse	NOUN
ejpam-3363	158	10	some	some	PRON
ejpam-3363	158	11	of	of	ADP
ejpam-3363	158	12	the	the	DET
ejpam-3363	158	13	standard	standard	ADJ
ejpam-3363	158	14	properties	property	NOUN
ejpam-3363	158	15	of	of	ADP
ejpam-3363	158	16	an	an	DET
ejpam-3363	158	17	integral	integral	ADJ
ejpam-3363	158	18	namely	namely	ADV
ejpam-3363	158	19	,	,	PUNCT
ejpam-3363	158	20	uniqueness	uniqueness	NOUN
ejpam-3363	158	21	of	of	ADP
ejpam-3363	158	22	an	an	DET
ejpam-3363	158	23	integral	integral	ADJ
ejpam-3363	158	24	,	,	PUNCT
ejpam-3363	158	25	linearity	linearity	NOUN
ejpam-3363	158	26	,	,	PUNCT
ejpam-3363	158	27	integrability	integrability	NOUN
ejpam-3363	158	28	on	on	ADP
ejpam-3363	158	29	every	every	DET
ejpam-3363	158	30	subinterval	subinterval	NOUN
ejpam-3363	158	31	of	of	ADP
ejpam-3363	158	32	[	[	X
ejpam-3363	158	33	0	0	NUM
ejpam-3363	158	34	,	,	PUNCT
ejpam-3363	158	35	t	t	X
ejpam-3363	158	36	]	]	PUNCT
ejpam-3363	158	37	,	,	PUNCT
ejpam-3363	158	38	the	the	DET
ejpam-3363	158	39	cauchy	cauchy	ADJ
ejpam-3363	158	40	criterion	criterion	NOUN
ejpam-3363	158	41	,	,	PUNCT
ejpam-3363	158	42	and	and	CCONJ
ejpam-3363	158	43	the	the	DET
ejpam-3363	158	44	saks	sak	NOUN
ejpam-3363	158	45	-	-	PUNCT
ejpam-3363	158	46	henstock	henstock	NUM
ejpam-3363	158	47	lemma	lemma	PROPN
ejpam-3363	158	48	.	.	PUNCT
ejpam-3363	159	1	the	the	DET
ejpam-3363	159	2	proofs	proof	NOUN
ejpam-3363	159	3	of	of	ADP
ejpam-3363	159	4	these	these	DET
ejpam-3363	159	5	results	result	NOUN
ejpam-3363	159	6	are	be	AUX
ejpam-3363	159	7	standard	standard	ADJ
ejpam-3363	159	8	in	in	ADP
ejpam-3363	159	9	henstock	henstock	NOUN
ejpam-3363	159	10	-	-	PUNCT
ejpam-3363	159	11	kurzweil	kurzweil	NOUN
ejpam-3363	159	12	integration	integration	NOUN
ejpam-3363	159	13	,	,	PUNCT
ejpam-3363	159	14	hence	hence	ADV
ejpam-3363	159	15	omitted	omit	VERB
ejpam-3363	159	16	.	.	PUNCT
ejpam-3363	160	1	(	(	PUNCT
ejpam-3363	160	2	i	i	NOUN
ejpam-3363	160	3	)	)	PUNCT
ejpam-3363	161	1	the	the	DET
ejpam-3363	161	2	i	i	PRON
ejpam-3363	161	3	m	m	VERB
ejpam-3363	161	4	integral	integral	ADJ
ejpam-3363	161	5	is	be	AUX
ejpam-3363	161	6	uniquely	uniquely	ADV
ejpam-3363	161	7	determined	determine	VERB
ejpam-3363	161	8	,	,	PUNCT
ejpam-3363	161	9	in	in	ADP
ejpam-3363	161	10	the	the	DET
ejpam-3363	161	11	sense	sense	NOUN
ejpam-3363	161	12	that	that	SCONJ
ejpam-3363	161	13	if	if	SCONJ
ejpam-3363	161	14	a1	a1	NOUN
ejpam-3363	161	15	and	and	CCONJ
ejpam-3363	161	16	a2	a2	PROPN
ejpam-3363	161	17	are	be	AUX
ejpam-3363	161	18	two	two	NUM
ejpam-3363	162	1	i	i	NOUN
ejpam-3363	162	2	m	m	VERB
ejpam-3363	162	3	integrals	integral	NOUN
ejpam-3363	162	4	of	of	ADP
ejpam-3363	162	5	f	f	PROPN
ejpam-3363	162	6	,	,	PUNCT
ejpam-3363	162	7	then	then	ADV
ejpam-3363	162	8	‖a1	‖a1	PUNCT
ejpam-3363	162	9	−a2‖l2(u	−a2‖l2(u	NOUN
ejpam-3363	162	10	,	,	PUNCT
ejpam-3363	162	11	v	v	NOUN
ejpam-3363	162	12	)	)	PUNCT
ejpam-3363	162	13	=	=	SYM
ejpam-3363	163	1	0	0	X
ejpam-3363	163	2	.	.	PUNCT
ejpam-3363	163	3	j.d	j.d	PROPN
ejpam-3363	163	4	.	.	PROPN
ejpam-3363	163	5	cagubcob	cagubcob	PROPN
ejpam-3363	163	6	,	,	PUNCT
ejpam-3363	163	7	m.	m.	NOUN
ejpam-3363	163	8	labendia	labendia	PROPN
ejpam-3363	163	9	/	/	SYM
ejpam-3363	163	10	eur	eur	PROPN
ejpam-3363	163	11	.	.	PUNCT
ejpam-3363	164	1	j.	j.	PROPN
ejpam-3363	164	2	pure	pure	PROPN
ejpam-3363	164	3	appl	appl	PROPN
ejpam-3363	164	4	.	.	PROPN
ejpam-3363	164	5	math	math	PROPN
ejpam-3363	164	6	,	,	PUNCT
ejpam-3363	164	7	12	12	NUM
ejpam-3363	164	8	(	(	PUNCT
ejpam-3363	164	9	1	1	NUM
ejpam-3363	164	10	)	)	PUNCT
ejpam-3363	164	11	(	(	PUNCT
ejpam-3363	164	12	2019	2019	NUM
ejpam-3363	164	13	)	)	PUNCT
ejpam-3363	164	14	,	,	PUNCT
ejpam-3363	164	15	101	101	NUM
ejpam-3363	164	16	-	-	SYM
ejpam-3363	164	17	117	117	NUM
ejpam-3363	164	18	107	107	NUM
ejpam-3363	164	19	(	(	PUNCT
ejpam-3363	164	20	ii	ii	NOUN
ejpam-3363	164	21	)	)	PUNCT
ejpam-3363	164	22	let	let	VERB
ejpam-3363	164	23	f	f	X
ejpam-3363	164	24	,	,	PUNCT
ejpam-3363	164	25	g	g	PROPN
ejpam-3363	164	26	∈	∈	PROPN
ejpam-3363	164	27	λim	λim	X
ejpam-3363	164	28	and	and	CCONJ
ejpam-3363	164	29	let	let	VERB
ejpam-3363	164	30	α	α	PRON
ejpam-3363	164	31	,	,	PUNCT
ejpam-3363	164	32	β	β	PROPN
ejpam-3363	164	33	∈	∈	PROPN
ejpam-3363	164	34	r.	r.	PROPN
ejpam-3363	164	35	then	then	ADV
ejpam-3363	164	36	αf	αf	VERB
ejpam-3363	164	37	+	+	NOUN
ejpam-3363	164	38	βg	βg	NOUN
ejpam-3363	164	39	∈	∈	PROPN
ejpam-3363	164	40	λim	λim	X
ejpam-3363	165	1	and	and	CCONJ
ejpam-3363	165	2	(	(	PUNCT
ejpam-3363	165	3	i	i	NOUN
ejpam-3363	165	4	m	m	PROPN
ejpam-3363	165	5	)	)	PUNCT
ejpam-3363	165	6	∫	∫	PROPN
ejpam-3363	165	7	t	t	PROPN
ejpam-3363	165	8	0	0	NUM
ejpam-3363	166	1	(	(	PUNCT
ejpam-3363	166	2	αf	αf	ADP
ejpam-3363	166	3	+	+	CCONJ
ejpam-3363	166	4	βg	βg	ADJ
ejpam-3363	166	5	)	)	PUNCT
ejpam-3363	166	6	dw	dw	NOUN
ejpam-3363	166	7	=	=	SYM
ejpam-3363	166	8	α	α	PROPN
ejpam-3363	166	9	·	·	PUNCT
ejpam-3363	166	10	(	(	PUNCT
ejpam-3363	166	11	i	i	NOUN
ejpam-3363	166	12	m	m	VERB
ejpam-3363	166	13	)	)	PUNCT
ejpam-3363	166	14	∫	∫	PROPN
ejpam-3363	167	1	t	t	PROPN
ejpam-3363	167	2	0	0	NUM
ejpam-3363	167	3	f	f	PROPN
ejpam-3363	167	4	dw	dw	PROPN
ejpam-3363	167	5	+	+	CCONJ
ejpam-3363	167	6	β	β	X
ejpam-3363	167	7	·	·	PUNCT
ejpam-3363	167	8	(	(	PUNCT
ejpam-3363	167	9	i	i	NOUN
ejpam-3363	167	10	m	m	VERB
ejpam-3363	167	11	)	)	PUNCT
ejpam-3363	168	1	∫	∫	PROPN
ejpam-3363	168	2	t	t	PROPN
ejpam-3363	168	3	0	0	NUM
ejpam-3363	168	4	g	g	PROPN
ejpam-3363	168	5	dw	dw	PROPN
ejpam-3363	168	6	.	.	PUNCT
ejpam-3363	168	7	(	(	PUNCT
ejpam-3363	168	8	iii	iii	X
ejpam-3363	168	9	)	)	PUNCT
ejpam-3363	168	10	cauchy	cauchy	NOUN
ejpam-3363	168	11	criterion	criterion	NOUN
ejpam-3363	168	12	.	.	PUNCT
ejpam-3363	169	1	a	a	DET
ejpam-3363	169	2	process	process	NOUN
ejpam-3363	169	3	f	f	PROPN
ejpam-3363	169	4	is	be	AUX
ejpam-3363	169	5	im	im	NOUN
ejpam-3363	169	6	-	-	NOUN
ejpam-3363	169	7	integrable	integrable	ADJ
ejpam-3363	169	8	on	on	ADP
ejpam-3363	169	9	[	[	X
ejpam-3363	169	10	0	0	NUM
ejpam-3363	169	11	,	,	PUNCT
ejpam-3363	169	12	t	t	X
ejpam-3363	169	13	]	]	PUNCT
ejpam-3363	169	14	if	if	SCONJ
ejpam-3363	169	15	and	and	CCONJ
ejpam-3363	169	16	only	only	ADV
ejpam-3363	169	17	if	if	SCONJ
ejpam-3363	169	18	for	for	ADP
ejpam-3363	169	19	every	every	DET
ejpam-3363	169	20	ε	ε	PROPN
ejpam-3363	169	21	>	>	X
ejpam-3363	169	22	0	0	PROPN
ejpam-3363	169	23	,	,	PUNCT
ejpam-3363	169	24	there	there	PRON
ejpam-3363	169	25	exist	exist	VERB
ejpam-3363	169	26	a	a	DET
ejpam-3363	169	27	positive	positive	ADJ
ejpam-3363	169	28	function	function	NOUN
ejpam-3363	169	29	δ	δ	PROPN
ejpam-3363	169	30	on	on	ADP
ejpam-3363	169	31	[	[	X
ejpam-3363	169	32	0	0	NUM
ejpam-3363	169	33	,	,	PUNCT
ejpam-3363	169	34	t	t	NOUN
ejpam-3363	169	35	]	]	PUNCT
ejpam-3363	169	36	and	and	CCONJ
ejpam-3363	169	37	a	a	DET
ejpam-3363	169	38	number	number	NOUN
ejpam-3363	169	39	η	η	X
ejpam-3363	169	40	>	>	X
ejpam-3363	169	41	0	0	NUM
ejpam-3363	170	1	such	such	ADJ
ejpam-3363	170	2	that	that	PRON
ejpam-3363	170	3	for	for	ADP
ejpam-3363	170	4	any	any	DET
ejpam-3363	170	5	two	two	NUM
ejpam-3363	170	6	(	(	PUNCT
ejpam-3363	170	7	δ	δ	PROPN
ejpam-3363	170	8	,	,	PUNCT
ejpam-3363	170	9	η)-fine	η)-fine	PROPN
ejpam-3363	170	10	belated	belate	VERB
ejpam-3363	170	11	mcshane	mcshane	PROPN
ejpam-3363	170	12	partial	partial	ADJ
ejpam-3363	170	13	divisions	division	NOUN
ejpam-3363	170	14	d1	d1	PROPN
ejpam-3363	170	15	and	and	CCONJ
ejpam-3363	170	16	d2	d2	PROPN
ejpam-3363	170	17	of	of	ADP
ejpam-3363	170	18	[	[	X
ejpam-3363	170	19	0	0	NUM
ejpam-3363	170	20	,	,	PUNCT
ejpam-3363	170	21	t	t	X
ejpam-3363	170	22	]	]	PUNCT
ejpam-3363	170	23	,	,	PUNCT
ejpam-3363	170	24	we	we	PRON
ejpam-3363	170	25	have	have	VERB
ejpam-3363	170	26	e	e	X
ejpam-3363	170	27	[	[	PUNCT
ejpam-3363	170	28	‖s(f	‖s(f	ADJ
ejpam-3363	170	29	,	,	PUNCT
ejpam-3363	170	30	d1	d1	PROPN
ejpam-3363	170	31	,	,	PUNCT
ejpam-3363	170	32	δ	δ	PROPN
ejpam-3363	170	33	,	,	PUNCT
ejpam-3363	170	34	η)−	η)−	PROPN
ejpam-3363	170	35	s(f	s(f	PROPN
ejpam-3363	170	36	,	,	PUNCT
ejpam-3363	170	37	d2	d2	PROPN
ejpam-3363	170	38	,	,	PUNCT
ejpam-3363	170	39	δ	δ	PROPN
ejpam-3363	170	40	,	,	PUNCT
ejpam-3363	170	41	η)‖2v	η)‖2v	X
ejpam-3363	170	42	]	]	PUNCT
ejpam-3363	171	1	<	<	X
ejpam-3363	171	2	ε	ε	PROPN
ejpam-3363	171	3	.	.	PUNCT
ejpam-3363	171	4	(	(	PUNCT
ejpam-3363	171	5	iv	iv	X
ejpam-3363	171	6	)	)	PUNCT
ejpam-3363	171	7	if	if	SCONJ
ejpam-3363	171	8	f	f	PROPN
ejpam-3363	171	9	is	be	AUX
ejpam-3363	171	10	im	im	NOUN
ejpam-3363	171	11	-	-	NOUN
ejpam-3363	171	12	integrable	integrable	ADJ
ejpam-3363	171	13	on	on	ADP
ejpam-3363	171	14	[	[	X
ejpam-3363	171	15	0	0	NUM
ejpam-3363	171	16	,	,	PUNCT
ejpam-3363	171	17	t	t	X
ejpam-3363	171	18	]	]	PUNCT
ejpam-3363	171	19	,	,	PUNCT
ejpam-3363	171	20	then	then	ADV
ejpam-3363	171	21	f	f	PROPN
ejpam-3363	171	22	is	be	AUX
ejpam-3363	171	23	im	im	NOUN
ejpam-3363	171	24	-	-	NOUN
ejpam-3363	171	25	integrable	integrable	ADJ
ejpam-3363	171	26	on	on	ADP
ejpam-3363	171	27	[	[	X
ejpam-3363	171	28	c	c	X
ejpam-3363	171	29	,	,	PUNCT
ejpam-3363	171	30	d	d	X
ejpam-3363	171	31	]	]	X
ejpam-3363	171	32	⊂	⊂	PROPN
ejpam-3363	172	1	[	[	X
ejpam-3363	172	2	0	0	NUM
ejpam-3363	172	3	,	,	PUNCT
ejpam-3363	172	4	t	t	X
ejpam-3363	172	5	]	]	PUNCT
ejpam-3363	172	6	.	.	PUNCT
ejpam-3363	173	1	(	(	PUNCT
ejpam-3363	173	2	v	v	NOUN
ejpam-3363	173	3	)	)	PUNCT
ejpam-3363	173	4	if	if	SCONJ
ejpam-3363	173	5	f	f	PROPN
ejpam-3363	173	6	is	be	AUX
ejpam-3363	173	7	im	im	NOUN
ejpam-3363	173	8	-	-	NOUN
ejpam-3363	173	9	integrable	integrable	ADJ
ejpam-3363	173	10	on	on	ADP
ejpam-3363	173	11	[	[	X
ejpam-3363	173	12	0	0	NUM
ejpam-3363	173	13	,	,	PUNCT
ejpam-3363	173	14	c	c	NOUN
ejpam-3363	173	15	]	]	PUNCT
ejpam-3363	173	16	and	and	CCONJ
ejpam-3363	173	17	[	[	X
ejpam-3363	173	18	c	c	X
ejpam-3363	173	19	,	,	PUNCT
ejpam-3363	173	20	t	t	NOUN
ejpam-3363	173	21	]	]	PUNCT
ejpam-3363	173	22	where	where	SCONJ
ejpam-3363	173	23	c	c	PROPN
ejpam-3363	173	24	∈	∈	PROPN
ejpam-3363	173	25	(	(	PUNCT
ejpam-3363	173	26	0	0	NUM
ejpam-3363	173	27	,	,	PUNCT
ejpam-3363	173	28	t	t	NOUN
ejpam-3363	173	29	)	)	PUNCT
ejpam-3363	173	30	,	,	PUNCT
ejpam-3363	173	31	then	then	ADV
ejpam-3363	173	32	f	f	PROPN
ejpam-3363	173	33	is	be	AUX
ejpam-3363	173	34	im	im	NOUN
ejpam-3363	173	35	-	-	NOUN
ejpam-3363	173	36	integrable	integrable	ADJ
ejpam-3363	173	37	on	on	ADP
ejpam-3363	173	38	[	[	X
ejpam-3363	173	39	0	0	NUM
ejpam-3363	173	40	,	,	PUNCT
ejpam-3363	173	41	t	t	NOUN
ejpam-3363	173	42	]	]	PUNCT
ejpam-3363	173	43	and	and	CCONJ
ejpam-3363	173	44	(	(	PUNCT
ejpam-3363	173	45	i	i	NOUN
ejpam-3363	173	46	m	m	VERB
ejpam-3363	173	47	)	)	PUNCT
ejpam-3363	174	1	∫	∫	PROPN
ejpam-3363	174	2	t	t	PROPN
ejpam-3363	174	3	0	0	NUM
ejpam-3363	175	1	f	f	PROPN
ejpam-3363	175	2	dw	dw	PROPN
ejpam-3363	175	3	=	=	PUNCT
ejpam-3363	175	4	(	(	PUNCT
ejpam-3363	175	5	i	i	NOUN
ejpam-3363	175	6	m	m	VERB
ejpam-3363	175	7	)	)	PUNCT
ejpam-3363	175	8	∫	∫	PROPN
ejpam-3363	176	1	c	c	NOUN
ejpam-3363	176	2	0	0	NUM
ejpam-3363	176	3	f	f	PROPN
ejpam-3363	176	4	dw	dw	PROPN
ejpam-3363	177	1	+	+	CCONJ
ejpam-3363	177	2	(	(	PUNCT
ejpam-3363	177	3	i	i	NOUN
ejpam-3363	177	4	m	m	PROPN
ejpam-3363	177	5	)	)	PUNCT
ejpam-3363	177	6	∫	∫	PROPN
ejpam-3363	178	1	t	t	PROPN
ejpam-3363	178	2	c	c	PROPN
ejpam-3363	178	3	f	f	PROPN
ejpam-3363	178	4	dw	dw	PROPN
ejpam-3363	178	5	.	.	PROPN
ejpam-3363	178	6	(	(	PUNCT
ejpam-3363	178	7	vi	vi	NOUN
ejpam-3363	178	8	)	)	PUNCT
ejpam-3363	178	9	sequential	sequential	ADJ
ejpam-3363	178	10	definition	definition	NOUN
ejpam-3363	178	11	.	.	PUNCT
ejpam-3363	179	1	a	a	DET
ejpam-3363	179	2	process	process	NOUN
ejpam-3363	179	3	f	f	PROPN
ejpam-3363	179	4	is	be	AUX
ejpam-3363	179	5	im	im	NOUN
ejpam-3363	179	6	-	-	NOUN
ejpam-3363	179	7	integrable	integrable	ADJ
ejpam-3363	179	8	on	on	ADP
ejpam-3363	179	9	[	[	X
ejpam-3363	179	10	0	0	NUM
ejpam-3363	179	11	,	,	PUNCT
ejpam-3363	179	12	t	t	X
ejpam-3363	179	13	]	]	PUNCT
ejpam-3363	179	14	if	if	SCONJ
ejpam-3363	179	15	and	and	CCONJ
ejpam-3363	179	16	only	only	ADV
ejpam-3363	179	17	if	if	SCONJ
ejpam-3363	179	18	there	there	PRON
ejpam-3363	179	19	exist	exist	VERB
ejpam-3363	179	20	a	a	DET
ejpam-3363	179	21	∈	∈	PROPN
ejpam-3363	179	22	l2(ω	l2(ω	PROPN
ejpam-3363	179	23	,	,	PUNCT
ejpam-3363	179	24	v	v	NOUN
ejpam-3363	179	25	)	)	PUNCT
ejpam-3363	179	26	,	,	PUNCT
ejpam-3363	179	27	a	a	DET
ejpam-3363	179	28	decreasing	decrease	VERB
ejpam-3363	179	29	sequence	sequence	NOUN
ejpam-3363	179	30	{	{	PUNCT
ejpam-3363	179	31	δn	δn	NOUN
ejpam-3363	179	32	}	}	PUNCT
ejpam-3363	179	33	of	of	ADP
ejpam-3363	179	34	positive	positive	ADJ
ejpam-3363	179	35	functions	function	NOUN
ejpam-3363	179	36	defined	define	VERB
ejpam-3363	179	37	on	on	ADP
ejpam-3363	179	38	[	[	X
ejpam-3363	179	39	0	0	NUM
ejpam-3363	179	40	,	,	PUNCT
ejpam-3363	179	41	t	t	X
ejpam-3363	179	42	]	]	PUNCT
ejpam-3363	179	43	,	,	PUNCT
ejpam-3363	179	44	and	and	CCONJ
ejpam-3363	179	45	a	a	DET
ejpam-3363	179	46	decreasing	decrease	VERB
ejpam-3363	179	47	sequence	sequence	NOUN
ejpam-3363	179	48	of	of	ADP
ejpam-3363	179	49	positive	positive	ADJ
ejpam-3363	179	50	numbers	number	NOUN
ejpam-3363	179	51	ηn	ηn	VERB
ejpam-3363	179	52	such	such	ADJ
ejpam-3363	179	53	that	that	PRON
ejpam-3363	179	54	for	for	ADP
ejpam-3363	179	55	any	any	DET
ejpam-3363	179	56	(	(	PUNCT
ejpam-3363	179	57	δn	δn	NOUN
ejpam-3363	179	58	,	,	PUNCT
ejpam-3363	179	59	ηn)-fine	ηn)-fine	PROPN
ejpam-3363	179	60	belated	belate	VERB
ejpam-3363	179	61	mcshane	mcshane	PROPN
ejpam-3363	179	62	partial	partial	ADJ
ejpam-3363	179	63	division	division	NOUN
ejpam-3363	179	64	dn	dn	NOUN
ejpam-3363	179	65	of	of	ADP
ejpam-3363	179	66	[	[	X
ejpam-3363	179	67	0	0	NUM
ejpam-3363	179	68	,	,	PUNCT
ejpam-3363	179	69	t	t	X
ejpam-3363	179	70	]	]	PUNCT
ejpam-3363	179	71	,	,	PUNCT
ejpam-3363	179	72	we	we	PRON
ejpam-3363	179	73	have	have	VERB
ejpam-3363	179	74	e	e	X
ejpam-3363	179	75	[	[	PUNCT
ejpam-3363	179	76	‖s(f	‖s(f	ADJ
ejpam-3363	179	77	,	,	PUNCT
ejpam-3363	179	78	dn	dn	NOUN
ejpam-3363	179	79	,	,	PUNCT
ejpam-3363	179	80	δn	δn	NOUN
ejpam-3363	179	81	,	,	PUNCT
ejpam-3363	179	82	ηn)−a‖2v	ηn)−a‖2v	PROPN
ejpam-3363	179	83	]	]	PUNCT
ejpam-3363	179	84	→	→	SYM
ejpam-3363	179	85	0	0	NUM
ejpam-3363	179	86	as	as	ADP
ejpam-3363	179	87	n→∞.	n→∞.	ADJ
ejpam-3363	179	88	in	in	ADP
ejpam-3363	179	89	this	this	DET
ejpam-3363	179	90	case	case	NOUN
ejpam-3363	179	91	,	,	PUNCT
ejpam-3363	179	92	a	a	PRON
ejpam-3363	179	93	:	:	PUNCT
ejpam-3363	179	94	=	=	SYM
ejpam-3363	179	95	(	(	PUNCT
ejpam-3363	179	96	i	i	NOUN
ejpam-3363	179	97	m	m	VERB
ejpam-3363	179	98	)	)	PUNCT
ejpam-3363	180	1	∫	∫	PROPN
ejpam-3363	180	2	t	t	PROPN
ejpam-3363	180	3	0	0	NUM
ejpam-3363	180	4	ft	ft	NOUN
ejpam-3363	180	5	dwt	dwt	PROPN
ejpam-3363	180	6	.	.	PUNCT
ejpam-3363	181	1	(	(	PUNCT
ejpam-3363	181	2	vii	vii	PROPN
ejpam-3363	181	3	)	)	PUNCT
ejpam-3363	181	4	saks	sak	NOUN
ejpam-3363	181	5	-	-	PUNCT
ejpam-3363	181	6	henstock	henstock	NOUN
ejpam-3363	181	7	lemma	lemma	PROPN
ejpam-3363	181	8	(	(	PUNCT
ejpam-3363	181	9	weak	weak	ADJ
ejpam-3363	181	10	version	version	NOUN
ejpam-3363	181	11	)	)	PUNCT
ejpam-3363	181	12	.	.	PUNCT
ejpam-3363	182	1	let	let	VERB
ejpam-3363	182	2	f	f	PRON
ejpam-3363	182	3	be	be	AUX
ejpam-3363	182	4	im	im	NOUN
ejpam-3363	182	5	-	-	NOUN
ejpam-3363	182	6	integrable	integrable	ADJ
ejpam-3363	182	7	on	on	ADP
ejpam-3363	182	8	[	[	X
ejpam-3363	182	9	0	0	NUM
ejpam-3363	182	10	,	,	PUNCT
ejpam-3363	182	11	t	t	NOUN
ejpam-3363	182	12	]	]	PUNCT
ejpam-3363	182	13	and	and	CCONJ
ejpam-3363	182	14	f	f	X
ejpam-3363	183	1	[	[	X
ejpam-3363	183	2	u	u	NOUN
ejpam-3363	183	3	,	,	PUNCT
ejpam-3363	183	4	v	v	NOUN
ejpam-3363	183	5	]	]	PUNCT
ejpam-3363	183	6	:	:	PUNCT
ejpam-3363	183	7	=	=	SYM
ejpam-3363	183	8	(	(	PUNCT
ejpam-3363	183	9	i	i	NOUN
ejpam-3363	183	10	m	m	VERB
ejpam-3363	183	11	)	)	PUNCT
ejpam-3363	183	12	∫	∫	PROPN
ejpam-3363	184	1	v	v	NUM
ejpam-3363	184	2	u	u	PROPN
ejpam-3363	184	3	f	f	PROPN
ejpam-3363	184	4	dw	dw	PROPN
ejpam-3363	184	5	for	for	ADP
ejpam-3363	184	6	any	any	DET
ejpam-3363	184	7	[	[	X
ejpam-3363	184	8	u	u	NOUN
ejpam-3363	184	9	,	,	PUNCT
ejpam-3363	184	10	v	v	ADP
ejpam-3363	184	11	]	]	X
ejpam-3363	184	12	⊂	⊂	PROPN
ejpam-3363	185	1	[	[	X
ejpam-3363	185	2	0	0	NUM
ejpam-3363	185	3	,	,	PUNCT
ejpam-3363	185	4	t	t	X
ejpam-3363	185	5	]	]	PUNCT
ejpam-3363	185	6	.	.	PUNCT
ejpam-3363	186	1	then	then	ADV
ejpam-3363	186	2	for	for	ADP
ejpam-3363	186	3	every	every	DET
ejpam-3363	186	4	ε	ε	PROPN
ejpam-3363	186	5	>	>	X
ejpam-3363	186	6	0	0	PROPN
ejpam-3363	186	7	,	,	PUNCT
ejpam-3363	186	8	there	there	PRON
ejpam-3363	186	9	exists	exist	VERB
ejpam-3363	186	10	a	a	DET
ejpam-3363	186	11	positive	positive	ADJ
ejpam-3363	186	12	function	function	NOUN
ejpam-3363	186	13	δ	δ	PROPN
ejpam-3363	186	14	on	on	ADP
ejpam-3363	186	15	[	[	X
ejpam-3363	186	16	0	0	NUM
ejpam-3363	186	17	,	,	PUNCT
ejpam-3363	186	18	t	t	X
ejpam-3363	186	19	]	]	PUNCT
ejpam-3363	186	20	such	such	ADJ
ejpam-3363	186	21	that	that	PRON
ejpam-3363	186	22	for	for	SCONJ
ejpam-3363	186	23	any	any	DET
ejpam-3363	186	24	δ	δ	NOUN
ejpam-3363	186	25	-	-	PUNCT
ejpam-3363	186	26	fine	fine	NOUN
ejpam-3363	186	27	belated	belate	VERB
ejpam-3363	186	28	mcshane	mcshane	PROPN
ejpam-3363	186	29	partial	partial	ADJ
ejpam-3363	186	30	division	division	NOUN
ejpam-3363	186	31	d	d	NOUN
ejpam-3363	186	32	=	=	PRON
ejpam-3363	186	33	{	{	PUNCT
ejpam-3363	186	34	(	(	PUNCT
ejpam-3363	186	35	[	[	X
ejpam-3363	186	36	u	u	NOUN
ejpam-3363	186	37	,	,	PUNCT
ejpam-3363	186	38	v	v	ADP
ejpam-3363	186	39	]	]	X
ejpam-3363	186	40	,	,	PUNCT
ejpam-3363	186	41	ξ	ξ	X
ejpam-3363	186	42	)	)	PUNCT
ejpam-3363	186	43	}	}	PUNCT
ejpam-3363	186	44	of	of	ADP
ejpam-3363	186	45	[	[	X
ejpam-3363	186	46	0	0	NUM
ejpam-3363	186	47	,	,	PUNCT
ejpam-3363	186	48	t	t	X
ejpam-3363	186	49	]	]	PUNCT
ejpam-3363	186	50	,	,	PUNCT
ejpam-3363	186	51	we	we	PRON
ejpam-3363	186	52	have	have	VERB
ejpam-3363	186	53	e	e	NOUN
ejpam-3363	186	54	[	[	X
ejpam-3363	186	55	∥∥∥(d	∥∥∥(d	X
ejpam-3363	186	56	)	)	PUNCT
ejpam-3363	186	57	∑	∑	PRON
ejpam-3363	186	58	{	{	PUNCT
ejpam-3363	186	59	fξ(wv	fξ(wv	NOUN
ejpam-3363	186	60	−wξ)−	−wξ)−	NOUN
ejpam-3363	186	61	f	f	X
ejpam-3363	187	1	[	[	X
ejpam-3363	187	2	u	u	NOUN
ejpam-3363	187	3	,	,	PUNCT
ejpam-3363	187	4	v	v	NOUN
ejpam-3363	187	5	]	]	X
ejpam-3363	187	6	}	}	PUNCT
ejpam-3363	187	7	∥∥∥2	∥∥∥2	NOUN
ejpam-3363	187	8	v	v	ADP
ejpam-3363	187	9	]	]	PUNCT
ejpam-3363	187	10	<	<	X
ejpam-3363	187	11	ε	ε	PROPN
ejpam-3363	187	12	.	.	PROPN
ejpam-3363	188	1	next	next	ADV
ejpam-3363	188	2	,	,	PUNCT
ejpam-3363	188	3	we	we	PRON
ejpam-3363	188	4	define	define	VERB
ejpam-3363	188	5	the	the	DET
ejpam-3363	188	6	concept	concept	NOUN
ejpam-3363	188	7	of	of	ADP
ejpam-3363	188	8	ac2[0	ac2[0	ADJ
ejpam-3363	188	9	,	,	PUNCT
ejpam-3363	188	10	t	t	PROPN
ejpam-3363	188	11	]	]	PUNCT
ejpam-3363	188	12	-property	-property	PROPN
ejpam-3363	188	13	,	,	PUNCT
ejpam-3363	188	14	a	a	DET
ejpam-3363	188	15	version	version	NOUN
ejpam-3363	188	16	of	of	ADP
ejpam-3363	188	17	absolute	absolute	ADJ
ejpam-3363	188	18	continuity	continuity	NOUN
ejpam-3363	188	19	.	.	PUNCT
ejpam-3363	189	1	definition	definition	NOUN
ejpam-3363	189	2	4	4	NUM
ejpam-3363	189	3	.	.	PUNCT
ejpam-3363	190	1	a	a	DET
ejpam-3363	190	2	function	function	NOUN
ejpam-3363	190	3	f	f	NOUN
ejpam-3363	190	4	:	:	PUNCT
ejpam-3363	190	5	j	j	PROPN
ejpam-3363	190	6	×	×	PROPN
ejpam-3363	190	7	ω→	ω→	NUM
ejpam-3363	190	8	v	v	NOUN
ejpam-3363	190	9	is	be	AUX
ejpam-3363	190	10	said	say	VERB
ejpam-3363	190	11	to	to	PART
ejpam-3363	190	12	be	be	AUX
ejpam-3363	190	13	belated	belate	VERB
ejpam-3363	190	14	mcshane	mcshane	PROPN
ejpam-3363	190	15	differentiable	differentiable	NOUN
ejpam-3363	190	16	at	at	ADP
ejpam-3363	190	17	ξ	ξ	PROPN
ejpam-3363	190	18	∈	∈	PROPN
ejpam-3363	191	1	[	[	X
ejpam-3363	191	2	0	0	NUM
ejpam-3363	191	3	,	,	PUNCT
ejpam-3363	191	4	t	t	NOUN
ejpam-3363	191	5	)	)	PUNCT
ejpam-3363	191	6	if	if	SCONJ
ejpam-3363	191	7	there	there	PRON
ejpam-3363	191	8	exists	exist	VERB
ejpam-3363	191	9	a	a	DET
ejpam-3363	191	10	random	random	ADJ
ejpam-3363	191	11	variable	variable	NOUN
ejpam-3363	191	12	fξ	fξ	PROPN
ejpam-3363	191	13	:	:	PUNCT
ejpam-3363	191	14	ω→	ω→	PUNCT
ejpam-3363	191	15	l(u	l(u	PROPN
ejpam-3363	191	16	,	,	PUNCT
ejpam-3363	191	17	v	v	NOUN
ejpam-3363	191	18	)	)	PUNCT
ejpam-3363	191	19	such	such	ADJ
ejpam-3363	191	20	that	that	PRON
ejpam-3363	191	21	for	for	ADP
ejpam-3363	191	22	all	all	DET
ejpam-3363	191	23	ε	ε	PROPN
ejpam-3363	191	24	>	>	X
ejpam-3363	191	25	0	0	PROPN
ejpam-3363	191	26	,	,	PUNCT
ejpam-3363	191	27	there	there	PRON
ejpam-3363	191	28	exists	exist	VERB
ejpam-3363	191	29	a	a	DET
ejpam-3363	191	30	positive	positive	ADJ
ejpam-3363	191	31	function	function	NOUN
ejpam-3363	191	32	δ	δ	PROPN
ejpam-3363	191	33	on	on	ADP
ejpam-3363	191	34	[	[	X
ejpam-3363	191	35	0	0	NUM
ejpam-3363	191	36	,	,	PUNCT
ejpam-3363	191	37	t	t	X
ejpam-3363	191	38	]	]	PUNCT
ejpam-3363	191	39	such	such	ADJ
ejpam-3363	191	40	that	that	SCONJ
ejpam-3363	191	41	for	for	SCONJ
ejpam-3363	191	42	all	all	DET
ejpam-3363	191	43	δ	δ	PROPN
ejpam-3363	191	44	-	-	PUNCT
ejpam-3363	191	45	fine	fine	NOUN
ejpam-3363	191	46	belated	belate	VERB
ejpam-3363	191	47	mcshane	mcshane	PROPN
ejpam-3363	191	48	interval	interval	NOUN
ejpam-3363	191	49	-	-	PUNCT
ejpam-3363	191	50	point	point	NOUN
ejpam-3363	191	51	pair	pair	NOUN
ejpam-3363	191	52	(	(	PUNCT
ejpam-3363	191	53	[	[	X
ejpam-3363	191	54	u	u	NOUN
ejpam-3363	191	55	,	,	PUNCT
ejpam-3363	191	56	v	v	ADP
ejpam-3363	191	57	]	]	X
ejpam-3363	191	58	,	,	PUNCT
ejpam-3363	191	59	ξ	ξ	X
ejpam-3363	191	60	)	)	PUNCT
ejpam-3363	191	61	of	of	ADP
ejpam-3363	191	62	[	[	X
ejpam-3363	191	63	0	0	NUM
ejpam-3363	191	64	,	,	PUNCT
ejpam-3363	191	65	t	t	X
ejpam-3363	191	66	]	]	PUNCT
ejpam-3363	191	67	,	,	PUNCT
ejpam-3363	191	68	e	e	X
ejpam-3363	191	69	[	[	PUNCT
ejpam-3363	192	1	‖fξ(wv	‖fξ(wv	ADJ
ejpam-3363	192	2	−wu)−	−wu)−	NOUN
ejpam-3363	192	3	f	f	NOUN
ejpam-3363	193	1	[	[	X
ejpam-3363	193	2	u	u	NOUN
ejpam-3363	193	3	,	,	PUNCT
ejpam-3363	193	4	v]‖2v	v]‖2v	X
ejpam-3363	193	5	]	]	PUNCT
ejpam-3363	193	6	<	<	X
ejpam-3363	193	7	ε(v	ε(v	PROPN
ejpam-3363	193	8	−	−	PROPN
ejpam-3363	193	9	u	u	NOUN
ejpam-3363	193	10	)	)	PUNCT
ejpam-3363	193	11	.	.	PUNCT
ejpam-3363	194	1	the	the	DET
ejpam-3363	194	2	random	random	ADJ
ejpam-3363	194	3	variable	variable	NOUN
ejpam-3363	194	4	fξ	fξ	NOUN
ejpam-3363	194	5	is	be	AUX
ejpam-3363	194	6	called	call	VERB
ejpam-3363	194	7	the	the	DET
ejpam-3363	194	8	belated	belate	VERB
ejpam-3363	194	9	mcshane	mcshane	PROPN
ejpam-3363	194	10	derivative	derivative	NOUN
ejpam-3363	194	11	of	of	ADP
ejpam-3363	194	12	f	f	PROPN
ejpam-3363	194	13	at	at	ADP
ejpam-3363	194	14	the	the	DET
ejpam-3363	194	15	point	point	NOUN
ejpam-3363	194	16	ξ	ξ	X
ejpam-3363	194	17	∈	∈	PROPN
ejpam-3363	195	1	[	[	X
ejpam-3363	195	2	0	0	NUM
ejpam-3363	195	3	,	,	PUNCT
ejpam-3363	195	4	t	t	NOUN
ejpam-3363	195	5	)	)	PUNCT
ejpam-3363	195	6	and	and	CCONJ
ejpam-3363	195	7	is	be	AUX
ejpam-3363	195	8	denoted	denote	VERB
ejpam-3363	195	9	by	by	ADP
ejpam-3363	195	10	dfξ	dfξ	NOUN
ejpam-3363	195	11	.	.	PUNCT
ejpam-3363	195	12	j.d	j.d	PROPN
ejpam-3363	195	13	.	.	PROPN
ejpam-3363	195	14	cagubcob	cagubcob	PROPN
ejpam-3363	195	15	,	,	PUNCT
ejpam-3363	195	16	m.	m.	NOUN
ejpam-3363	195	17	labendia	labendia	PROPN
ejpam-3363	195	18	/	/	SYM
ejpam-3363	195	19	eur	eur	PROPN
ejpam-3363	195	20	.	.	PUNCT
ejpam-3363	196	1	j.	j.	PROPN
ejpam-3363	196	2	pure	pure	PROPN
ejpam-3363	196	3	appl	appl	PROPN
ejpam-3363	196	4	.	.	PROPN
ejpam-3363	196	5	math	math	PROPN
ejpam-3363	196	6	,	,	PUNCT
ejpam-3363	196	7	12	12	NUM
ejpam-3363	196	8	(	(	PUNCT
ejpam-3363	196	9	1	1	NUM
ejpam-3363	196	10	)	)	PUNCT
ejpam-3363	196	11	(	(	PUNCT
ejpam-3363	196	12	2019	2019	NUM
ejpam-3363	196	13	)	)	PUNCT
ejpam-3363	196	14	,	,	PUNCT
ejpam-3363	196	15	101	101	NUM
ejpam-3363	196	16	-	-	SYM
ejpam-3363	196	17	117	117	NUM
ejpam-3363	196	18	108	108	NUM
ejpam-3363	196	19	we	we	PRON
ejpam-3363	196	20	note	note	VERB
ejpam-3363	196	21	that	that	SCONJ
ejpam-3363	196	22	we	we	PRON
ejpam-3363	196	23	write	write	VERB
ejpam-3363	196	24	f	f	PROPN
ejpam-3363	197	1	[	[	X
ejpam-3363	197	2	u	u	NOUN
ejpam-3363	197	3	,	,	PUNCT
ejpam-3363	197	4	v	v	NOUN
ejpam-3363	197	5	]	]	PUNCT
ejpam-3363	197	6	instead	instead	ADV
ejpam-3363	197	7	of	of	ADP
ejpam-3363	197	8	f	f	PROPN
ejpam-3363	197	9	(	(	PUNCT
ejpam-3363	197	10	[	[	X
ejpam-3363	197	11	u	u	NOUN
ejpam-3363	197	12	,	,	PUNCT
ejpam-3363	197	13	v	v	NOUN
ejpam-3363	197	14	]	]	PUNCT
ejpam-3363	197	15	)	)	PUNCT
ejpam-3363	197	16	.	.	PUNCT
ejpam-3363	198	1	definition	definition	NOUN
ejpam-3363	198	2	5	5	NUM
ejpam-3363	198	3	.	.	PUNCT
ejpam-3363	199	1	a	a	DET
ejpam-3363	199	2	function	function	NOUN
ejpam-3363	199	3	f	f	NOUN
ejpam-3363	199	4	:	:	PUNCT
ejpam-3363	199	5	j	j	PROPN
ejpam-3363	199	6	×	×	PROPN
ejpam-3363	199	7	ω→	ω→	NUM
ejpam-3363	199	8	v	v	PROPN
ejpam-3363	199	9	(	(	PUNCT
ejpam-3363	199	10	i	i	NOUN
ejpam-3363	199	11	)	)	PUNCT
ejpam-3363	199	12	is	be	AUX
ejpam-3363	199	13	said	say	VERB
ejpam-3363	199	14	to	to	PART
ejpam-3363	199	15	be	be	AUX
ejpam-3363	199	16	ac2[0	ac2[0	ADJ
ejpam-3363	199	17	,	,	PUNCT
ejpam-3363	199	18	t	t	X
ejpam-3363	199	19	]	]	PUNCT
ejpam-3363	199	20	if	if	SCONJ
ejpam-3363	199	21	for	for	ADP
ejpam-3363	199	22	every	every	DET
ejpam-3363	199	23	ε	ε	PROPN
ejpam-3363	199	24	>	>	X
ejpam-3363	199	25	0	0	PROPN
ejpam-3363	199	26	,	,	PUNCT
ejpam-3363	199	27	there	there	PRON
ejpam-3363	199	28	exists	exist	VERB
ejpam-3363	199	29	η	η	PROPN
ejpam-3363	199	30	>	>	X
ejpam-3363	199	31	0	0	NUM
ejpam-3363	199	32	such	such	ADJ
ejpam-3363	199	33	that	that	PRON
ejpam-3363	199	34	for	for	ADP
ejpam-3363	199	35	any	any	DET
ejpam-3363	199	36	finite	finite	ADJ
ejpam-3363	199	37	collection	collection	NOUN
ejpam-3363	200	1	d	d	NOUN
ejpam-3363	200	2	=	=	PRON
ejpam-3363	200	3	{	{	PUNCT
ejpam-3363	200	4	[	[	X
ejpam-3363	200	5	u	u	NOUN
ejpam-3363	200	6	,	,	PUNCT
ejpam-3363	200	7	v	v	NOUN
ejpam-3363	200	8	]	]	X
ejpam-3363	200	9	}	}	PUNCT
ejpam-3363	200	10	of	of	ADP
ejpam-3363	200	11	non	non	ADJ
ejpam-3363	200	12	-	-	ADJ
ejpam-3363	200	13	overlapping	overlapping	ADJ
ejpam-3363	200	14	intervals	interval	NOUN
ejpam-3363	200	15	[	[	X
ejpam-3363	200	16	u	u	NOUN
ejpam-3363	200	17	,	,	PUNCT
ejpam-3363	200	18	v	v	NOUN
ejpam-3363	200	19	]	]	X
ejpam-3363	200	20	∈	∈	PROPN
ejpam-3363	200	21	j	j	PROPN
ejpam-3363	200	22	with	with	ADP
ejpam-3363	200	23	(	(	PUNCT
ejpam-3363	200	24	d	d	NOUN
ejpam-3363	200	25	)	)	PUNCT
ejpam-3363	200	26	∑	∑	PUNCT
ejpam-3363	200	27	(	(	PUNCT
ejpam-3363	200	28	v−	v−	NOUN
ejpam-3363	200	29	u	u	NOUN
ejpam-3363	200	30	)	)	PUNCT
ejpam-3363	200	31	≤	≤	PROPN
ejpam-3363	200	32	η	η	PROPN
ejpam-3363	200	33	,	,	PUNCT
ejpam-3363	200	34	we	we	PRON
ejpam-3363	200	35	have	have	VERB
ejpam-3363	200	36	e	e	NOUN
ejpam-3363	200	37	[	[	X
ejpam-3363	200	38	∥∥∥(d	∥∥∥(d	PUNCT
ejpam-3363	200	39	)	)	PUNCT
ejpam-3363	200	40	∑	∑	PUNCT
ejpam-3363	200	41	f	f	PROPN
ejpam-3363	201	1	[	[	X
ejpam-3363	201	2	u	u	NOUN
ejpam-3363	201	3	,	,	PUNCT
ejpam-3363	201	4	v	v	NOUN
ejpam-3363	201	5	]	]	X
ejpam-3363	201	6	∥∥∥2	∥∥∥2	NOUN
ejpam-3363	201	7	v	v	ADP
ejpam-3363	201	8	]	]	PUNCT
ejpam-3363	201	9	<	<	X
ejpam-3363	201	10	ε	ε	PROPN
ejpam-3363	201	11	;	;	PUNCT
ejpam-3363	201	12	(	(	PUNCT
ejpam-3363	201	13	ii	ii	NOUN
ejpam-3363	201	14	)	)	PUNCT
ejpam-3363	201	15	has	have	VERB
ejpam-3363	201	16	the	the	DET
ejpam-3363	201	17	orthogonal	orthogonal	ADJ
ejpam-3363	201	18	increment	increment	NOUN
ejpam-3363	201	19	property	property	NOUN
ejpam-3363	201	20	if	if	SCONJ
ejpam-3363	201	21	for	for	ADP
ejpam-3363	201	22	all	all	DET
ejpam-3363	201	23	non	non	ADJ
ejpam-3363	201	24	-	-	ADJ
ejpam-3363	201	25	overlapping	overlapping	ADJ
ejpam-3363	201	26	intervals	interval	NOUN
ejpam-3363	201	27	[	[	X
ejpam-3363	201	28	a	a	X
ejpam-3363	201	29	,	,	PUNCT
ejpam-3363	201	30	b	b	NOUN
ejpam-3363	201	31	]	]	X
ejpam-3363	201	32	,	,	PUNCT
ejpam-3363	201	33	[	[	X
ejpam-3363	201	34	u	u	NOUN
ejpam-3363	201	35	,	,	PUNCT
ejpam-3363	201	36	v	v	ADP
ejpam-3363	201	37	]	]	X
ejpam-3363	201	38	⊂	⊂	PROPN
ejpam-3363	202	1	[	[	X
ejpam-3363	202	2	0	0	NUM
ejpam-3363	202	3	,	,	PUNCT
ejpam-3363	202	4	t	t	X
ejpam-3363	202	5	]	]	PUNCT
ejpam-3363	202	6	,	,	PUNCT
ejpam-3363	202	7	e	e	X
ejpam-3363	203	1	[	[	X
ejpam-3363	203	2	〈	〈	PROPN
ejpam-3363	203	3	f	f	X
ejpam-3363	203	4	[	[	X
ejpam-3363	203	5	a	a	X
ejpam-3363	203	6	,	,	PUNCT
ejpam-3363	203	7	b	b	NOUN
ejpam-3363	203	8	]	]	X
ejpam-3363	203	9	,	,	PUNCT
ejpam-3363	203	10	f	f	PROPN
ejpam-3363	204	1	[	[	X
ejpam-3363	204	2	u	u	NOUN
ejpam-3363	204	3	,	,	PUNCT
ejpam-3363	204	4	v	v	ADP
ejpam-3363	204	5	]	]	X
ejpam-3363	204	6	〉	〉	NOUN
ejpam-3363	204	7	]	]	X
ejpam-3363	204	8	=	=	PUNCT
ejpam-3363	204	9	0	0	X
ejpam-3363	204	10	.	.	PUNCT
ejpam-3363	205	1	the	the	DET
ejpam-3363	205	2	proof	proof	NOUN
ejpam-3363	205	3	of	of	ADP
ejpam-3363	205	4	the	the	DET
ejpam-3363	205	5	following	follow	VERB
ejpam-3363	205	6	theorem	theorem	NOUN
ejpam-3363	205	7	is	be	AUX
ejpam-3363	205	8	parallel	parallel	ADJ
ejpam-3363	205	9	to	to	ADP
ejpam-3363	205	10	the	the	DET
ejpam-3363	205	11	proof	proof	NOUN
ejpam-3363	205	12	in	in	ADP
ejpam-3363	205	13	[	[	X
ejpam-3363	205	14	5	5	NUM
ejpam-3363	205	15	]	]	PUNCT
ejpam-3363	205	16	.	.	PUNCT
ejpam-3363	206	1	theorem	theorem	NOUN
ejpam-3363	206	2	1	1	NUM
ejpam-3363	206	3	.	.	PUNCT
ejpam-3363	207	1	[	[	X
ejpam-3363	207	2	5	5	X
ejpam-3363	207	3	]	]	PUNCT
ejpam-3363	207	4	let	let	VERB
ejpam-3363	207	5	f	f	PRON
ejpam-3363	207	6	be	be	AUX
ejpam-3363	207	7	im	im	NOUN
ejpam-3363	207	8	-	-	NOUN
ejpam-3363	207	9	integrable	integrable	ADJ
ejpam-3363	207	10	on	on	ADP
ejpam-3363	207	11	[	[	X
ejpam-3363	207	12	0	0	NUM
ejpam-3363	207	13	,	,	PUNCT
ejpam-3363	207	14	t	t	NOUN
ejpam-3363	207	15	]	]	PUNCT
ejpam-3363	207	16	and	and	CCONJ
ejpam-3363	207	17	define	define	VERB
ejpam-3363	207	18	f	f	PROPN
ejpam-3363	208	1	[	[	X
ejpam-3363	208	2	u	u	NOUN
ejpam-3363	208	3	,	,	PUNCT
ejpam-3363	208	4	v	v	NOUN
ejpam-3363	208	5	]	]	PUNCT
ejpam-3363	208	6	:	:	PUNCT
ejpam-3363	208	7	=	=	SYM
ejpam-3363	208	8	(	(	PUNCT
ejpam-3363	208	9	i	i	NOUN
ejpam-3363	208	10	m	m	VERB
ejpam-3363	208	11	)	)	PUNCT
ejpam-3363	208	12	∫	∫	PROPN
ejpam-3363	208	13	v	v	NUM
ejpam-3363	208	14	u	u	NOUN
ejpam-3363	208	15	fsdws	fsdws	VERB
ejpam-3363	208	16	for	for	SCONJ
ejpam-3363	208	17	all	all	DET
ejpam-3363	208	18	[	[	X
ejpam-3363	208	19	u	u	NOUN
ejpam-3363	208	20	,	,	PUNCT
ejpam-3363	208	21	v	v	ADP
ejpam-3363	208	22	]	]	X
ejpam-3363	208	23	⊂	⊂	PROPN
ejpam-3363	209	1	[	[	X
ejpam-3363	209	2	0	0	NUM
ejpam-3363	209	3	,	,	PUNCT
ejpam-3363	209	4	t	t	X
ejpam-3363	209	5	]	]	PUNCT
ejpam-3363	209	6	.	.	PUNCT
ejpam-3363	210	1	then	then	ADV
ejpam-3363	210	2	f	f	PROPN
ejpam-3363	210	3	is	be	AUX
ejpam-3363	210	4	ac2[0	ac2[0	ADJ
ejpam-3363	210	5	,	,	PUNCT
ejpam-3363	210	6	t	t	X
ejpam-3363	210	7	]	]	PUNCT
ejpam-3363	210	8	and	and	CCONJ
ejpam-3363	210	9	has	have	VERB
ejpam-3363	210	10	the	the	DET
ejpam-3363	210	11	orthogonal	orthogonal	ADJ
ejpam-3363	210	12	increment	increment	NOUN
ejpam-3363	210	13	property	property	NOUN
ejpam-3363	210	14	.	.	PUNCT
ejpam-3363	211	1	lemma	lemma	PROPN
ejpam-3363	211	2	3	3	X
ejpam-3363	211	3	.	.	PUNCT
ejpam-3363	212	1	[	[	X
ejpam-3363	212	2	5	5	X
ejpam-3363	212	3	]	]	PUNCT
ejpam-3363	212	4	let	let	VERB
ejpam-3363	212	5	f	f	PRON
ejpam-3363	212	6	:	:	PUNCT
ejpam-3363	213	1	[	[	X
ejpam-3363	213	2	0	0	NUM
ejpam-3363	213	3	,	,	PUNCT
ejpam-3363	213	4	t	t	X
ejpam-3363	213	5	]	]	PUNCT
ejpam-3363	213	6	×	×	PROPN
ejpam-3363	213	7	ω	ω	PROPN
ejpam-3363	213	8	→	→	SYM
ejpam-3363	213	9	l(u	l(u	PROPN
ejpam-3363	213	10	,	,	PUNCT
ejpam-3363	213	11	v	v	NOUN
ejpam-3363	213	12	)	)	PUNCT
ejpam-3363	213	13	be	be	AUX
ejpam-3363	213	14	an	an	DET
ejpam-3363	213	15	adapted	adapt	VERB
ejpam-3363	213	16	process	process	NOUN
ejpam-3363	213	17	,	,	PUNCT
ejpam-3363	213	18	f	f	PROPN
ejpam-3363	213	19	:	:	PUNCT
ejpam-3363	213	20	j	j	PROPN
ejpam-3363	213	21	×	×	PROPN
ejpam-3363	213	22	ω	ω	PROPN
ejpam-3363	213	23	→	→	SYM
ejpam-3363	213	24	v	v	NOUN
ejpam-3363	213	25	with	with	ADP
ejpam-3363	213	26	orthogonal	orthogonal	ADJ
ejpam-3363	213	27	increment	increment	NOUN
ejpam-3363	213	28	property	property	NOUN
ejpam-3363	213	29	and	and	CCONJ
ejpam-3363	213	30	{	{	PUNCT
ejpam-3363	213	31	[	[	X
ejpam-3363	213	32	ui	ui	NOUN
ejpam-3363	213	33	,	,	PUNCT
ejpam-3363	213	34	vi]}ni=1	vi]}ni=1	PROPN
ejpam-3363	213	35	be	be	AUX
ejpam-3363	213	36	a	a	DET
ejpam-3363	213	37	finite	finite	ADJ
ejpam-3363	213	38	collection	collection	NOUN
ejpam-3363	213	39	of	of	ADP
ejpam-3363	213	40	non	non	ADJ
ejpam-3363	213	41	-	-	ADJ
ejpam-3363	213	42	overlapping	overlapping	ADJ
ejpam-3363	213	43	subintervals	subinterval	NOUN
ejpam-3363	213	44	of	of	ADP
ejpam-3363	213	45	[	[	X
ejpam-3363	213	46	0	0	NUM
ejpam-3363	213	47	,	,	PUNCT
ejpam-3363	213	48	t	t	X
ejpam-3363	213	49	]	]	PUNCT
ejpam-3363	213	50	.	.	PUNCT
ejpam-3363	214	1	then	then	ADV
ejpam-3363	214	2	e	e	X
ejpam-3363	214	3	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-3363	214	4	n∑	n∑	X
ejpam-3363	214	5	i=1	i=1	PROPN
ejpam-3363	214	6	{	{	PUNCT
ejpam-3363	214	7	fξi(wvi	fξi(wvi	NOUN
ejpam-3363	214	8	−wui)−	−wui)−	NOUN
ejpam-3363	214	9	f	f	PROPN
ejpam-3363	215	1	[	[	X
ejpam-3363	215	2	ui	ui	PROPN
ejpam-3363	215	3	,	,	PUNCT
ejpam-3363	215	4	vi	vi	PROPN
ejpam-3363	215	5	]	]	X
ejpam-3363	215	6	}	}	PUNCT
ejpam-3363	215	7	∥∥∥∥∥	∥∥∥∥∥	VERB
ejpam-3363	215	8	2	2	NUM
ejpam-3363	215	9	v	v	NOUN
ejpam-3363	215	10			NOUN
ejpam-3363	215	11	=	=	PUNCT
ejpam-3363	216	1	n∑	n∑	NOUN
ejpam-3363	216	2	i=1	i=1	PROPN
ejpam-3363	217	1	e	e	X
ejpam-3363	217	2	[	[	PUNCT
ejpam-3363	217	3	‖fξi(wvi	‖fξi(wvi	X
ejpam-3363	217	4	−wui)−	−wui)−	NOUN
ejpam-3363	217	5	f	f	PROPN
ejpam-3363	218	1	[	[	X
ejpam-3363	218	2	ui	ui	PROPN
ejpam-3363	218	3	,	,	PUNCT
ejpam-3363	218	4	vi]‖2v	vi]‖2v	X
ejpam-3363	218	5	]	]	PUNCT
ejpam-3363	218	6	.	.	PUNCT
ejpam-3363	219	1	lemma	lemma	PROPN
ejpam-3363	219	2	4	4	X
ejpam-3363	219	3	.	.	PUNCT
ejpam-3363	220	1	let	let	VERB
ejpam-3363	220	2	f	f	PROPN
ejpam-3363	220	3	∈	∈	PROPN
ejpam-3363	220	4	λim	λim	PROPN
ejpam-3363	220	5	.	.	PUNCT
ejpam-3363	221	1	then	then	ADV
ejpam-3363	221	2	for	for	ADP
ejpam-3363	221	3	every	every	DET
ejpam-3363	221	4	ε	ε	PROPN
ejpam-3363	221	5	>	>	X
ejpam-3363	221	6	0	0	PROPN
ejpam-3363	221	7	,	,	PUNCT
ejpam-3363	221	8	there	there	PRON
ejpam-3363	221	9	exist	exist	VERB
ejpam-3363	221	10	a	a	DET
ejpam-3363	221	11	positive	positive	ADJ
ejpam-3363	221	12	function	function	NOUN
ejpam-3363	221	13	δ	δ	PROPN
ejpam-3363	221	14	on	on	ADP
ejpam-3363	221	15	[	[	X
ejpam-3363	221	16	0	0	NUM
ejpam-3363	221	17	,	,	PUNCT
ejpam-3363	221	18	t	t	NOUN
ejpam-3363	221	19	]	]	PUNCT
ejpam-3363	221	20	and	and	CCONJ
ejpam-3363	221	21	a	a	DET
ejpam-3363	221	22	positive	positive	ADJ
ejpam-3363	221	23	number	number	NOUN
ejpam-3363	221	24	η	η	NOUN
ejpam-3363	221	25	such	such	ADJ
ejpam-3363	221	26	that	that	SCONJ
ejpam-3363	221	27	e	e	X
ejpam-3363	221	28	[	[	X
ejpam-3363	221	29	∥∥∥(d	∥∥∥(d	X
ejpam-3363	221	30	)	)	PUNCT
ejpam-3363	221	31	∑	∑	PUNCT
ejpam-3363	221	32	fξ(wv	fξ(wv	NOUN
ejpam-3363	221	33	−wu	−wu	NUM
ejpam-3363	221	34	)	)	PUNCT
ejpam-3363	221	35	∥∥∥2	∥∥∥2	NOUN
ejpam-3363	221	36	v	v	ADP
ejpam-3363	221	37	]	]	PUNCT
ejpam-3363	221	38	<	<	X
ejpam-3363	221	39	ε	ε	PROPN
ejpam-3363	221	40	for	for	SCONJ
ejpam-3363	221	41	any	any	DET
ejpam-3363	221	42	δ	δ	PROPN
ejpam-3363	221	43	-	-	PUNCT
ejpam-3363	221	44	fine	fine	NOUN
ejpam-3363	221	45	belated	belate	VERB
ejpam-3363	221	46	mcshane	mcshane	PROPN
ejpam-3363	221	47	partial	partial	ADJ
ejpam-3363	221	48	division	division	NOUN
ejpam-3363	221	49	d	d	NOUN
ejpam-3363	221	50	=	=	PRON
ejpam-3363	221	51	{	{	PUNCT
ejpam-3363	221	52	(	(	PUNCT
ejpam-3363	221	53	[	[	X
ejpam-3363	221	54	u	u	NOUN
ejpam-3363	221	55	,	,	PUNCT
ejpam-3363	221	56	v	v	ADP
ejpam-3363	221	57	]	]	X
ejpam-3363	221	58	,	,	PUNCT
ejpam-3363	221	59	ξ	ξ	X
ejpam-3363	221	60	)	)	PUNCT
ejpam-3363	221	61	}	}	PUNCT
ejpam-3363	221	62	of	of	ADP
ejpam-3363	221	63	[	[	X
ejpam-3363	221	64	0	0	NUM
ejpam-3363	221	65	,	,	PUNCT
ejpam-3363	221	66	t	t	X
ejpam-3363	221	67	]	]	PUNCT
ejpam-3363	221	68	with	with	ADP
ejpam-3363	221	69	(	(	PUNCT
ejpam-3363	221	70	d	d	NOUN
ejpam-3363	221	71	)	)	PUNCT
ejpam-3363	221	72	∑	∑	PUNCT
ejpam-3363	221	73	(	(	PUNCT
ejpam-3363	221	74	v	v	ADP
ejpam-3363	221	75	−	−	PROPN
ejpam-3363	221	76	u	u	NOUN
ejpam-3363	221	77	)	)	PUNCT
ejpam-3363	221	78	≤	≤	PROPN
ejpam-3363	221	79	η	η	PROPN
ejpam-3363	221	80	.	.	PROPN
ejpam-3363	221	81	proof	proof	NOUN
ejpam-3363	221	82	.	.	PUNCT
ejpam-3363	222	1	let	let	VERB
ejpam-3363	222	2	ε	ε	PROPN
ejpam-3363	222	3	>	>	X
ejpam-3363	222	4	0	0	PUNCT
ejpam-3363	222	5	be	be	AUX
ejpam-3363	222	6	given	give	VERB
ejpam-3363	222	7	.	.	PUNCT
ejpam-3363	223	1	then	then	ADV
ejpam-3363	223	2	there	there	PRON
ejpam-3363	223	3	exist	exist	VERB
ejpam-3363	223	4	a	a	DET
ejpam-3363	223	5	positive	positive	ADJ
ejpam-3363	223	6	function	function	NOUN
ejpam-3363	223	7	δ	δ	PROPN
ejpam-3363	223	8	on	on	ADP
ejpam-3363	223	9	[	[	X
ejpam-3363	223	10	0	0	NUM
ejpam-3363	223	11	,	,	PUNCT
ejpam-3363	223	12	t	t	NOUN
ejpam-3363	223	13	]	]	PUNCT
ejpam-3363	223	14	and	and	CCONJ
ejpam-3363	223	15	a	a	DET
ejpam-3363	223	16	number	number	NOUN
ejpam-3363	223	17	η	η	X
ejpam-3363	223	18	>	>	X
ejpam-3363	223	19	0	0	NUM
ejpam-3363	223	20	such	such	ADJ
ejpam-3363	223	21	that	that	PRON
ejpam-3363	223	22	for	for	ADP
ejpam-3363	223	23	any	any	DET
ejpam-3363	223	24	(	(	PUNCT
ejpam-3363	223	25	δ	δ	PROPN
ejpam-3363	223	26	,	,	PUNCT
ejpam-3363	223	27	η)-fone	η)-fone	NOUN
ejpam-3363	223	28	belated	belate	VERB
ejpam-3363	223	29	mcshane	mcshane	PROPN
ejpam-3363	223	30	partial	partial	ADJ
ejpam-3363	223	31	division	division	NOUN
ejpam-3363	223	32	p	p	NOUN
ejpam-3363	223	33	of	of	ADP
ejpam-3363	223	34	[	[	X
ejpam-3363	223	35	0	0	NUM
ejpam-3363	223	36	,	,	PUNCT
ejpam-3363	223	37	t	t	X
ejpam-3363	223	38	]	]	PUNCT
ejpam-3363	223	39	,	,	PUNCT
ejpam-3363	223	40	wehave	wehave	NOUN
ejpam-3363	223	41	e	e	PROPN
ejpam-3363	223	42	[	[	X
ejpam-3363	223	43	∥∥∥∥s(f	∥∥∥∥s(f	PROPN
ejpam-3363	223	44	,	,	PUNCT
ejpam-3363	223	45	p	p	X
ejpam-3363	223	46	,	,	PUNCT
ejpam-3363	223	47	δ	δ	PROPN
ejpam-3363	223	48	,	,	PUNCT
ejpam-3363	223	49	η)−	η)−	PROPN
ejpam-3363	223	50	(	(	PUNCT
ejpam-3363	223	51	i	i	NOUN
ejpam-3363	223	52	m	m	PROPN
ejpam-3363	223	53	)	)	PUNCT
ejpam-3363	224	1	∫	∫	PROPN
ejpam-3363	224	2	t	t	PROPN
ejpam-3363	224	3	0	0	NUM
ejpam-3363	225	1	ftdwt	ftdwt	PROPN
ejpam-3363	225	2	∥∥∥∥2	∥∥∥∥2	PROPN
ejpam-3363	225	3	v	v	ADP
ejpam-3363	225	4	]	]	PUNCT
ejpam-3363	225	5	<	<	X
ejpam-3363	225	6	ε	ε	PROPN
ejpam-3363	225	7	4	4	NUM
ejpam-3363	225	8	.	.	PUNCT
ejpam-3363	226	1	j.d	j.d	PROPN
ejpam-3363	226	2	.	.	PROPN
ejpam-3363	226	3	cagubcob	cagubcob	PROPN
ejpam-3363	226	4	,	,	PUNCT
ejpam-3363	226	5	m.	m.	NOUN
ejpam-3363	226	6	labendia	labendia	PROPN
ejpam-3363	226	7	/	/	SYM
ejpam-3363	226	8	eur	eur	PROPN
ejpam-3363	226	9	.	.	PUNCT
ejpam-3363	227	1	j.	j.	PROPN
ejpam-3363	227	2	pure	pure	PROPN
ejpam-3363	227	3	appl	appl	PROPN
ejpam-3363	227	4	.	.	PROPN
ejpam-3363	227	5	math	math	PROPN
ejpam-3363	227	6	,	,	PUNCT
ejpam-3363	227	7	12	12	NUM
ejpam-3363	227	8	(	(	PUNCT
ejpam-3363	227	9	1	1	NUM
ejpam-3363	227	10	)	)	PUNCT
ejpam-3363	227	11	(	(	PUNCT
ejpam-3363	227	12	2019	2019	NUM
ejpam-3363	227	13	)	)	PUNCT
ejpam-3363	227	14	,	,	PUNCT
ejpam-3363	227	15	101	101	NUM
ejpam-3363	227	16	-	-	SYM
ejpam-3363	227	17	117	117	NUM
ejpam-3363	227	18	109	109	NUM
ejpam-3363	227	19	let	let	VERB
ejpam-3363	227	20	d	d	NOUN
ejpam-3363	227	21	=	=	PRON
ejpam-3363	227	22	{	{	PUNCT
ejpam-3363	227	23	(	(	PUNCT
ejpam-3363	227	24	[	[	X
ejpam-3363	227	25	u	u	NOUN
ejpam-3363	227	26	,	,	PUNCT
ejpam-3363	227	27	v	v	ADP
ejpam-3363	227	28	]	]	X
ejpam-3363	227	29	,	,	PUNCT
ejpam-3363	227	30	ξ	ξ	X
ejpam-3363	227	31	)	)	PUNCT
ejpam-3363	227	32	}	}	PUNCT
ejpam-3363	227	33	be	be	AUX
ejpam-3363	227	34	a	a	DET
ejpam-3363	227	35	δ	δ	NOUN
ejpam-3363	227	36	-	-	PUNCT
ejpam-3363	227	37	fine	fine	NOUN
ejpam-3363	227	38	belated	belate	VERB
ejpam-3363	227	39	mcshane	mcshane	PROPN
ejpam-3363	227	40	partial	partial	ADJ
ejpam-3363	227	41	division	division	NOUN
ejpam-3363	227	42	of	of	ADP
ejpam-3363	227	43	[	[	X
ejpam-3363	227	44	0	0	NUM
ejpam-3363	227	45	,	,	PUNCT
ejpam-3363	227	46	t	t	X
ejpam-3363	227	47	]	]	PUNCT
ejpam-3363	227	48	with	with	ADP
ejpam-3363	227	49	(	(	PUNCT
ejpam-3363	227	50	d	d	NOUN
ejpam-3363	227	51	)	)	PUNCT
ejpam-3363	227	52	∑	∑	PUNCT
ejpam-3363	227	53	(	(	PUNCT
ejpam-3363	227	54	v−	v−	NOUN
ejpam-3363	227	55	u	u	NOUN
ejpam-3363	227	56	)	)	PUNCT
ejpam-3363	227	57	≤	≤	PROPN
ejpam-3363	227	58	η	η	PROPN
ejpam-3363	227	59	.	.	PROPN
ejpam-3363	227	60	construct	construct	VERB
ejpam-3363	227	61	a	a	DET
ejpam-3363	227	62	(	(	PUNCT
ejpam-3363	227	63	δ	δ	PROPN
ejpam-3363	227	64	,	,	PUNCT
ejpam-3363	227	65	η)-fine	η)-fine	PROPN
ejpam-3363	227	66	belated	belate	VERB
ejpam-3363	227	67	mcshane	mcshane	PROPN
ejpam-3363	227	68	partial	partial	ADJ
ejpam-3363	227	69	division	division	NOUN
ejpam-3363	227	70	of	of	ADP
ejpam-3363	227	71	[	[	X
ejpam-3363	227	72	0	0	NUM
ejpam-3363	227	73	,	,	PUNCT
ejpam-3363	227	74	t	t	X
ejpam-3363	227	75	]	]	PUNCT
ejpam-3363	227	76	.	.	PUNCT
ejpam-3363	228	1	by	by	ADP
ejpam-3363	228	2	assumption	assumption	NOUN
ejpam-3363	228	3	,	,	PUNCT
ejpam-3363	228	4	e	e	X
ejpam-3363	228	5	[	[	X
ejpam-3363	228	6	∥∥∥∥(d	∥∥∥∥(d	PROPN
ejpam-3363	228	7	∪d1	∪d1	PROPN
ejpam-3363	228	8	)	)	PUNCT
ejpam-3363	228	9	∑	∑	PUNCT
ejpam-3363	228	10	fξ(wv	fξ(wv	VERB
ejpam-3363	228	11	−wu)−	−wu)−	NOUN
ejpam-3363	228	12	(	(	PUNCT
ejpam-3363	228	13	i	i	NOUN
ejpam-3363	228	14	m	m	PROPN
ejpam-3363	228	15	)	)	PUNCT
ejpam-3363	229	1	∫	∫	PROPN
ejpam-3363	229	2	t	t	PROPN
ejpam-3363	229	3	0	0	NUM
ejpam-3363	230	1	ftdwt	ftdwt	PROPN
ejpam-3363	230	2	∥∥∥∥2	∥∥∥∥2	PROPN
ejpam-3363	230	3	v	v	ADP
ejpam-3363	230	4	]	]	PUNCT
ejpam-3363	230	5	<	<	X
ejpam-3363	230	6	ε	ε	PROPN
ejpam-3363	230	7	4	4	NUM
ejpam-3363	230	8	.	.	PUNCT
ejpam-3363	231	1	hence	hence	ADV
ejpam-3363	231	2	,	,	PUNCT
ejpam-3363	231	3	e	e	X
ejpam-3363	231	4	[	[	X
ejpam-3363	231	5	∥∥∥(d	∥∥∥(d	X
ejpam-3363	231	6	)	)	PUNCT
ejpam-3363	231	7	∑	∑	PUNCT
ejpam-3363	231	8	fξ(wv	fξ(wv	NOUN
ejpam-3363	231	9	−wu	−wu	NUM
ejpam-3363	231	10	)	)	PUNCT
ejpam-3363	231	11	∥∥∥2	∥∥∥2	NOUN
ejpam-3363	231	12	v	v	ADP
ejpam-3363	231	13	]	]	PUNCT
ejpam-3363	231	14	≤	≤	NUM
ejpam-3363	231	15	2e	2e	NOUN
ejpam-3363	231	16	[	[	X
ejpam-3363	231	17	∥∥∥∥(d	∥∥∥∥(d	PROPN
ejpam-3363	231	18	∪d1	∪d1	PROPN
ejpam-3363	231	19	)	)	PUNCT
ejpam-3363	231	20	∑	∑	PUNCT
ejpam-3363	231	21	fξ(wv	fξ(wv	VERB
ejpam-3363	231	22	−wu)−	−wu)−	NOUN
ejpam-3363	231	23	(	(	PUNCT
ejpam-3363	231	24	i	i	NOUN
ejpam-3363	231	25	m	m	PROPN
ejpam-3363	231	26	)	)	PUNCT
ejpam-3363	232	1	∫	∫	PROPN
ejpam-3363	232	2	t	t	PROPN
ejpam-3363	232	3	0	0	NUM
ejpam-3363	233	1	ftdwt	ftdwt	PROPN
ejpam-3363	233	2	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-3363	233	3	v	v	ADP
ejpam-3363	233	4	]	]	PUNCT
ejpam-3363	233	5	+	+	CCONJ
ejpam-3363	233	6	2e	2e	PROPN
ejpam-3363	233	7	[	[	NOUN
ejpam-3363	233	8	∥∥∥∥(im	∥∥∥∥(im	NOUN
ejpam-3363	233	9	)	)	PUNCT
ejpam-3363	233	10	∫	∫	PROPN
ejpam-3363	234	1	t	t	PROPN
ejpam-3363	234	2	0	0	NUM
ejpam-3363	234	3	ftdwt	ftdwt	PROPN
ejpam-3363	234	4	−	−	PROPN
ejpam-3363	234	5	(	(	PUNCT
ejpam-3363	234	6	d1	d1	PROPN
ejpam-3363	234	7	)	)	PUNCT
ejpam-3363	234	8	∑	∑	PUNCT
ejpam-3363	234	9	fξ(wv	fξ(wv	VERB
ejpam-3363	234	10	−wu	−wu	NOUN
ejpam-3363	234	11	)	)	PUNCT
ejpam-3363	234	12	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-3363	234	13	v	v	ADP
ejpam-3363	234	14	]	]	PUNCT
ejpam-3363	234	15	2	2	NUM
ejpam-3363	234	16	(	(	PUNCT
ejpam-3363	234	17	ε	ε	PROPN
ejpam-3363	234	18	4	4	NUM
ejpam-3363	234	19	)	)	PUNCT
ejpam-3363	235	1	+	+	CCONJ
ejpam-3363	235	2	2	2	NUM
ejpam-3363	235	3	(	(	PUNCT
ejpam-3363	235	4	ε	ε	PROPN
ejpam-3363	235	5	4	4	NUM
ejpam-3363	235	6	)	)	PUNCT
ejpam-3363	235	7	=	=	SYM
ejpam-3363	235	8	ε	ε	PROPN
ejpam-3363	235	9	.	.	PUNCT
ejpam-3363	235	10	(	(	PUNCT
ejpam-3363	235	11	6	6	NUM
ejpam-3363	235	12	)	)	PUNCT
ejpam-3363	235	13	this	this	PRON
ejpam-3363	235	14	proves	prove	VERB
ejpam-3363	235	15	the	the	DET
ejpam-3363	235	16	lemma	lemma	PROPN
ejpam-3363	235	17	.	.	PUNCT
ejpam-3363	236	1	theorem	theorem	PROPN
ejpam-3363	236	2	2	2	NUM
ejpam-3363	236	3	.	.	PUNCT
ejpam-3363	236	4	a	a	DET
ejpam-3363	236	5	process	process	NOUN
ejpam-3363	237	1	f	f	X
ejpam-3363	237	2	:	:	PUNCT
ejpam-3363	238	1	[	[	X
ejpam-3363	238	2	0	0	NUM
ejpam-3363	238	3	,	,	PUNCT
ejpam-3363	238	4	t	t	X
ejpam-3363	238	5	]	]	X
ejpam-3363	238	6	×	×	PROPN
ejpam-3363	238	7	ω→	ω→	SYM
ejpam-3363	238	8	l(u	l(u	PROPN
ejpam-3363	238	9	,	,	PUNCT
ejpam-3363	238	10	v	v	NOUN
ejpam-3363	238	11	)	)	PUNCT
ejpam-3363	238	12	is	be	AUX
ejpam-3363	238	13	im	im	NOUN
ejpam-3363	238	14	-	-	PUNCT
ejpam-3363	238	15	integrable	integrable	ADJ
ejpam-3363	238	16	if	if	SCONJ
ejpam-3363	238	17	and	and	CCONJ
ejpam-3363	238	18	only	only	ADV
ejpam-3363	238	19	if	if	SCONJ
ejpam-3363	238	20	(	(	PUNCT
ejpam-3363	238	21	i	i	NOUN
ejpam-3363	238	22	)	)	PUNCT
ejpam-3363	238	23	there	there	PRON
ejpam-3363	238	24	exists	exist	VERB
ejpam-3363	238	25	an	an	DET
ejpam-3363	238	26	ac2[0	ac2[0	NOUN
ejpam-3363	238	27	,	,	PUNCT
ejpam-3363	238	28	t	t	PROPN
ejpam-3363	238	29	]	]	PUNCT
ejpam-3363	238	30	function	function	NOUN
ejpam-3363	239	1	f	f	NOUN
ejpam-3363	239	2	:	:	PUNCT
ejpam-3363	239	3	j	j	PROPN
ejpam-3363	239	4	×	×	PROPN
ejpam-3363	239	5	ω→	ω→	PROPN
ejpam-3363	239	6	v	v	PROPN
ejpam-3363	239	7	and	and	CCONJ
ejpam-3363	239	8	(	(	PUNCT
ejpam-3363	239	9	ii	ii	NOUN
ejpam-3363	239	10	)	)	PUNCT
ejpam-3363	239	11	for	for	ADP
ejpam-3363	239	12	every	every	DET
ejpam-3363	239	13	ε	ε	PROPN
ejpam-3363	239	14	>	>	X
ejpam-3363	239	15	0	0	PROPN
ejpam-3363	239	16	,	,	PUNCT
ejpam-3363	239	17	there	there	PRON
ejpam-3363	239	18	exist	exist	VERB
ejpam-3363	239	19	a	a	DET
ejpam-3363	239	20	positive	positive	ADJ
ejpam-3363	239	21	function	function	NOUN
ejpam-3363	239	22	δ	δ	PROPN
ejpam-3363	239	23	on	on	ADP
ejpam-3363	239	24	[	[	X
ejpam-3363	239	25	0	0	NUM
ejpam-3363	239	26	,	,	PUNCT
ejpam-3363	239	27	t	t	X
ejpam-3363	239	28	]	]	PUNCT
ejpam-3363	239	29	such	such	ADJ
ejpam-3363	239	30	that	that	SCONJ
ejpam-3363	239	31	whenever	whenever	SCONJ
ejpam-3363	239	32	d	d	NOUN
ejpam-3363	239	33	=	=	PRON
ejpam-3363	239	34	{	{	PUNCT
ejpam-3363	239	35	(	(	PUNCT
ejpam-3363	239	36	[	[	X
ejpam-3363	239	37	u	u	NOUN
ejpam-3363	239	38	,	,	PUNCT
ejpam-3363	239	39	v	v	ADP
ejpam-3363	239	40	]	]	X
ejpam-3363	239	41	,	,	PUNCT
ejpam-3363	239	42	ξ	ξ	X
ejpam-3363	239	43	)	)	PUNCT
ejpam-3363	239	44	}	}	PUNCT
ejpam-3363	239	45	is	be	AUX
ejpam-3363	239	46	a	a	DET
ejpam-3363	239	47	δ	δ	NOUN
ejpam-3363	239	48	-	-	PUNCT
ejpam-3363	239	49	fine	fine	NOUN
ejpam-3363	239	50	belated	belate	VERB
ejpam-3363	239	51	mcshane	mcshane	PROPN
ejpam-3363	239	52	partial	partial	ADJ
ejpam-3363	239	53	division	division	NOUN
ejpam-3363	239	54	of	of	ADP
ejpam-3363	239	55	[	[	X
ejpam-3363	239	56	0	0	NUM
ejpam-3363	239	57	,	,	PUNCT
ejpam-3363	239	58	t	t	X
ejpam-3363	239	59	]	]	PUNCT
ejpam-3363	239	60	,	,	PUNCT
ejpam-3363	239	61	we	we	PRON
ejpam-3363	239	62	have	have	VERB
ejpam-3363	239	63	e	e	NOUN
ejpam-3363	239	64	[	[	X
ejpam-3363	239	65	∥∥∥(d	∥∥∥(d	X
ejpam-3363	239	66	)	)	PUNCT
ejpam-3363	239	67	∑	∑	PUNCT
ejpam-3363	239	68	{	{	PUNCT
ejpam-3363	239	69	fξ(wv	fξ(wv	VERB
ejpam-3363	239	70	−wu)−	−wu)−	ADP
ejpam-3363	239	71	f	f	NOUN
ejpam-3363	240	1	[	[	X
ejpam-3363	240	2	u	u	NOUN
ejpam-3363	240	3	,	,	PUNCT
ejpam-3363	240	4	v	v	NOUN
ejpam-3363	240	5	]	]	X
ejpam-3363	240	6	}	}	PUNCT
ejpam-3363	240	7	∥∥∥2	∥∥∥2	NOUN
ejpam-3363	240	8	v	v	ADP
ejpam-3363	240	9	]	]	PUNCT
ejpam-3363	240	10	<	<	X
ejpam-3363	240	11	ε	ε	PROPN
ejpam-3363	240	12	.	.	PUNCT
ejpam-3363	240	13	proof	proof	NOUN
ejpam-3363	240	14	.	.	PUNCT
ejpam-3363	240	15	suppose	suppose	VERB
ejpam-3363	240	16	that	that	SCONJ
ejpam-3363	240	17	f	f	PROPN
ejpam-3363	240	18	∈	∈	PROPN
ejpam-3363	240	19	λim	λim	PROPN
ejpam-3363	240	20	.	.	PUNCT
ejpam-3363	241	1	by	by	ADP
ejpam-3363	241	2	the	the	DET
ejpam-3363	241	3	saks	sak	NOUN
ejpam-3363	241	4	-	-	PUNCT
ejpam-3363	241	5	henstock	henstock	NOUN
ejpam-3363	241	6	lemma	lemma	PROPN
ejpam-3363	241	7	for	for	ADP
ejpam-3363	241	8	i	i	PROPN
ejpam-3363	241	9	m	m	VERB
ejpam-3363	241	10	integral	integral	ADJ
ejpam-3363	241	11	,	,	PUNCT
ejpam-3363	241	12	(	(	PUNCT
ejpam-3363	241	13	ii	ii	NOUN
ejpam-3363	241	14	)	)	PUNCT
ejpam-3363	241	15	holds	hold	VERB
ejpam-3363	241	16	.	.	PUNCT
ejpam-3363	242	1	next	next	ADV
ejpam-3363	242	2	we	we	PRON
ejpam-3363	242	3	show	show	VERB
ejpam-3363	242	4	that	that	SCONJ
ejpam-3363	242	5	f	f	PROPN
ejpam-3363	242	6	is	be	AUX
ejpam-3363	242	7	ac2[0	ac2[0	ADJ
ejpam-3363	242	8	,	,	PUNCT
ejpam-3363	242	9	t	t	X
ejpam-3363	242	10	]	]	PUNCT
ejpam-3363	242	11	.	.	PUNCT
ejpam-3363	243	1	let	let	VERB
ejpam-3363	243	2	ε	ε	PROPN
ejpam-3363	243	3	>	>	X
ejpam-3363	243	4	0	0	PUNCT
ejpam-3363	243	5	be	be	AUX
ejpam-3363	243	6	given	give	VERB
ejpam-3363	243	7	.	.	PUNCT
ejpam-3363	244	1	by	by	ADP
ejpam-3363	244	2	lemma	lemma	PROPN
ejpam-3363	244	3	4	4	NUM
ejpam-3363	244	4	,	,	PUNCT
ejpam-3363	244	5	there	there	PRON
ejpam-3363	244	6	exist	exist	VERB
ejpam-3363	244	7	a	a	DET
ejpam-3363	244	8	positive	positive	ADJ
ejpam-3363	244	9	function	function	NOUN
ejpam-3363	244	10	δ	δ	PROPN
ejpam-3363	244	11	on	on	ADP
ejpam-3363	244	12	[	[	X
ejpam-3363	244	13	0	0	NUM
ejpam-3363	244	14	,	,	PUNCT
ejpam-3363	244	15	t	t	NOUN
ejpam-3363	244	16	]	]	PUNCT
ejpam-3363	244	17	and	and	CCONJ
ejpam-3363	244	18	a	a	DET
ejpam-3363	244	19	number	number	NOUN
ejpam-3363	244	20	η	η	X
ejpam-3363	244	21	>	>	X
ejpam-3363	244	22	0	0	NUM
ejpam-3363	244	23	such	such	ADJ
ejpam-3363	244	24	that	that	SCONJ
ejpam-3363	244	25	e	e	X
ejpam-3363	244	26	[	[	X
ejpam-3363	244	27	∥∥∥(d	∥∥∥(d	X
ejpam-3363	244	28	)	)	PUNCT
ejpam-3363	244	29	∑	∑	PUNCT
ejpam-3363	244	30	fξ(wv	fξ(wv	NOUN
ejpam-3363	244	31	−wu	−wu	NUM
ejpam-3363	244	32	)	)	PUNCT
ejpam-3363	244	33	∥∥∥2	∥∥∥2	NOUN
ejpam-3363	244	34	v	v	ADP
ejpam-3363	244	35	]	]	PUNCT
ejpam-3363	244	36	<	<	X
ejpam-3363	244	37	ε	ε	PROPN
ejpam-3363	244	38	4	4	NUM
ejpam-3363	244	39	for	for	SCONJ
ejpam-3363	244	40	any	any	DET
ejpam-3363	244	41	δ	δ	NOUN
ejpam-3363	244	42	-	-	PUNCT
ejpam-3363	244	43	fine	fine	NOUN
ejpam-3363	244	44	belated	belate	VERB
ejpam-3363	244	45	mcshane	mcshane	PROPN
ejpam-3363	244	46	partial	partial	ADJ
ejpam-3363	244	47	division	division	NOUN
ejpam-3363	244	48	d	d	NOUN
ejpam-3363	244	49	=	=	PRON
ejpam-3363	244	50	{	{	PUNCT
ejpam-3363	244	51	(	(	PUNCT
ejpam-3363	244	52	[	[	X
ejpam-3363	244	53	u	u	NOUN
ejpam-3363	244	54	,	,	PUNCT
ejpam-3363	244	55	v	v	ADP
ejpam-3363	244	56	]	]	X
ejpam-3363	244	57	,	,	PUNCT
ejpam-3363	244	58	ξ	ξ	X
ejpam-3363	244	59	)	)	PUNCT
ejpam-3363	244	60	}	}	PUNCT
ejpam-3363	244	61	of	of	ADP
ejpam-3363	244	62	[	[	X
ejpam-3363	244	63	0	0	NUM
ejpam-3363	244	64	,	,	PUNCT
ejpam-3363	244	65	t	t	X
ejpam-3363	244	66	]	]	PUNCT
ejpam-3363	244	67	with	with	ADP
ejpam-3363	244	68	(	(	PUNCT
ejpam-3363	244	69	d	d	NOUN
ejpam-3363	244	70	∑	∑	PROPN
ejpam-3363	244	71	(	(	PUNCT
ejpam-3363	244	72	v	v	ADP
ejpam-3363	244	73	−	−	PROPN
ejpam-3363	244	74	u	u	NOUN
ejpam-3363	244	75	)	)	PUNCT
ejpam-3363	244	76	)	)	PUNCT
ejpam-3363	244	77	≤	≤	PROPN
ejpam-3363	245	1	η	η	PROPN
ejpam-3363	245	2	.	.	PROPN
ejpam-3363	246	1	let	let	VERB
ejpam-3363	246	2	{	{	PUNCT
ejpam-3363	246	3	[	[	X
ejpam-3363	246	4	aj	aj	PROPN
ejpam-3363	246	5	,	,	PUNCT
ejpam-3363	246	6	bj	bj	ADP
ejpam-3363	246	7	]	]	PUNCT
ejpam-3363	246	8	}	}	PUNCT
ejpam-3363	246	9	mj=1	mj=1	NOUN
ejpam-3363	246	10	be	be	VERB
ejpam-3363	246	11	a	a	DET
ejpam-3363	246	12	finite	finite	ADJ
ejpam-3363	246	13	collection	collection	NOUN
ejpam-3363	246	14	of	of	ADP
ejpam-3363	246	15	disjoint	disjoint	NOUN
ejpam-3363	246	16	subintervals	subinterval	NOUN
ejpam-3363	246	17	[	[	X
ejpam-3363	246	18	aj	aj	PROPN
ejpam-3363	246	19	,	,	PUNCT
ejpam-3363	246	20	bj	bj	VERB
ejpam-3363	246	21	]	]	PUNCT
ejpam-3363	246	22	∈	∈	PROPN
ejpam-3363	247	1	j	j	PROPN
ejpam-3363	247	2	with∑m	with∑m	PRON
ejpam-3363	247	3	j=1(bj	j=1(bj	PROPN
ejpam-3363	247	4	−aj	−aj	NOUN
ejpam-3363	247	5	)	)	PUNCT
ejpam-3363	247	6	≤	≤	PROPN
ejpam-3363	247	7	η	η	PROPN
ejpam-3363	247	8	.	.	PROPN
ejpam-3363	247	9	note	note	VERB
ejpam-3363	247	10	that	that	SCONJ
ejpam-3363	247	11	f	f	PROPN
ejpam-3363	247	12	is	be	AUX
ejpam-3363	247	13	also	also	ADV
ejpam-3363	247	14	im	im	PART
ejpam-3363	247	15	-	-	PUNCT
ejpam-3363	247	16	integrable	integrable	ADJ
ejpam-3363	247	17	on[aj	on[aj	ADJ
ejpam-3363	247	18	,	,	PUNCT
ejpam-3363	247	19	bj	bj	VERB
ejpam-3363	247	20	]	]	PUNCT
ejpam-3363	247	21	for	for	ADP
ejpam-3363	247	22	all	all	DET
ejpam-3363	247	23	j.	j.	PROPN
ejpam-3363	247	24	this	this	PRON
ejpam-3363	247	25	means	mean	VERB
ejpam-3363	247	26	that	that	SCONJ
ejpam-3363	247	27	for	for	ADP
ejpam-3363	247	28	all	all	DET
ejpam-3363	247	29	j	j	NOUN
ejpam-3363	247	30	,	,	PUNCT
ejpam-3363	247	31	there	there	PRON
ejpam-3363	247	32	exist	exist	VERB
ejpam-3363	247	33	a	a	DET
ejpam-3363	247	34	positive	positive	ADJ
ejpam-3363	247	35	function	function	NOUN
ejpam-3363	247	36	δj	δj	ADP
ejpam-3363	247	37	on	on	ADP
ejpam-3363	247	38	[	[	X
ejpam-3363	247	39	aj	aj	PROPN
ejpam-3363	247	40	,	,	PUNCT
ejpam-3363	247	41	bj	bj	VERB
ejpam-3363	247	42	]	]	PUNCT
ejpam-3363	247	43	and	and	CCONJ
ejpam-3363	247	44	a	a	DET
ejpam-3363	247	45	number	number	NOUN
ejpam-3363	247	46	ηj	ηj	ADP
ejpam-3363	247	47	>	>	X
ejpam-3363	247	48	0	0	NUM
ejpam-3363	247	49	such	such	ADJ
ejpam-3363	247	50	that	that	PRON
ejpam-3363	247	51	for	for	ADP
ejpam-3363	247	52	any	any	PRON
ejpam-3363	247	53	(	(	PUNCT
ejpam-3363	247	54	δj	δj	NOUN
ejpam-3363	247	55	,	,	PUNCT
ejpam-3363	247	56	ηj)-fine	ηj)-fine	NOUN
ejpam-3363	247	57	belated	belate	VERB
ejpam-3363	247	58	mcshane	mcshane	PROPN
ejpam-3363	247	59	partial	partial	ADJ
ejpam-3363	247	60	division	division	NOUN
ejpam-3363	247	61	dj	dj	NOUN
ejpam-3363	247	62	of	of	ADP
ejpam-3363	247	63	[	[	X
ejpam-3363	247	64	aj	aj	PROPN
ejpam-3363	247	65	,	,	PUNCT
ejpam-3363	247	66	bj	bj	ADP
ejpam-3363	247	67	]	]	PUNCT
ejpam-3363	247	68	,	,	PUNCT
ejpam-3363	247	69	we	we	PRON
ejpam-3363	247	70	have	have	VERB
ejpam-3363	247	71	e	e	X
ejpam-3363	247	72	[	[	PUNCT
ejpam-3363	247	73	‖s(f	‖s(f	ADJ
ejpam-3363	247	74	,	,	PUNCT
ejpam-3363	247	75	dj	dj	NOUN
ejpam-3363	247	76	,	,	PUNCT
ejpam-3363	247	77	δj	δj	NOUN
ejpam-3363	247	78	,	,	PUNCT
ejpam-3363	247	79	ηj)−	ηj)−	NOUN
ejpam-3363	247	80	f	f	PROPN
ejpam-3363	248	1	[	[	X
ejpam-3363	248	2	aj	aj	PROPN
ejpam-3363	248	3	,	,	PUNCT
ejpam-3363	248	4	bj	bj	ADP
ejpam-3363	248	5	]	]	PUNCT
ejpam-3363	248	6	‖2v	‖2v	X
ejpam-3363	248	7	]	]	PUNCT
ejpam-3363	248	8	<	<	X
ejpam-3363	248	9	ε	ε	PROPN
ejpam-3363	248	10	4	4	NUM
ejpam-3363	248	11	·	·	SYM
ejpam-3363	248	12	22j	22j	NOUN
ejpam-3363	248	13	.	.	PUNCT
ejpam-3363	249	1	j.d	j.d	PROPN
ejpam-3363	249	2	.	.	PROPN
ejpam-3363	249	3	cagubcob	cagubcob	PROPN
ejpam-3363	249	4	,	,	PUNCT
ejpam-3363	249	5	m.	m.	NOUN
ejpam-3363	249	6	labendia	labendia	PROPN
ejpam-3363	249	7	/	/	SYM
ejpam-3363	249	8	eur	eur	PROPN
ejpam-3363	249	9	.	.	PUNCT
ejpam-3363	250	1	j.	j.	PROPN
ejpam-3363	250	2	pure	pure	PROPN
ejpam-3363	250	3	appl	appl	PROPN
ejpam-3363	250	4	.	.	PROPN
ejpam-3363	250	5	math	math	PROPN
ejpam-3363	250	6	,	,	PUNCT
ejpam-3363	250	7	12	12	NUM
ejpam-3363	250	8	(	(	PUNCT
ejpam-3363	250	9	1	1	NUM
ejpam-3363	250	10	)	)	PUNCT
ejpam-3363	250	11	(	(	PUNCT
ejpam-3363	250	12	2019	2019	NUM
ejpam-3363	250	13	)	)	PUNCT
ejpam-3363	250	14	,	,	PUNCT
ejpam-3363	250	15	101	101	NUM
ejpam-3363	250	16	-	-	SYM
ejpam-3363	250	17	117	117	NUM
ejpam-3363	250	18	110	110	NUM
ejpam-3363	250	19	we	we	PRON
ejpam-3363	250	20	can	can	AUX
ejpam-3363	250	21	choose	choose	VERB
ejpam-3363	250	22	{	{	PUNCT
ejpam-3363	250	23	δj}mj=1	δj}mj=1	PROPN
ejpam-3363	250	24	and	and	CCONJ
ejpam-3363	250	25	{	{	PUNCT
ejpam-3363	250	26	ηj}mj=1	ηj}mj=1	X
ejpam-3363	250	27	such	such	ADJ
ejpam-3363	250	28	that	that	PRON
ejpam-3363	250	29	δj(ξ	δj(ξ	NOUN
ejpam-3363	250	30	)	)	PUNCT
ejpam-3363	250	31	≤	≤	NOUN
ejpam-3363	250	32	δ(ξ	δ(ξ	NOUN
ejpam-3363	250	33	)	)	PUNCT
ejpam-3363	250	34	for	for	ADP
ejpam-3363	250	35	all	all	DET
ejpam-3363	250	36	j	j	PROPN
ejpam-3363	250	37	and	and	CCONJ
ejpam-3363	250	38	∑m	∑m	PROPN
ejpam-3363	250	39	j=1	j=1	PROPN
ejpam-3363	250	40	ηj	ηj	ADP
ejpam-3363	250	41	≤	≤	PROPN
ejpam-3363	250	42	η	η	PROPN
ejpam-3363	250	43	.	.	PROPN
ejpam-3363	251	1	let	let	VERB
ejpam-3363	251	2	p	p	NOUN
ejpam-3363	251	3	=	=	PUNCT
ejpam-3363	251	4	d1	d1	PROPN
ejpam-3363	251	5	∪d2	∪d2	ADJ
ejpam-3363	251	6	∪	∪	ADP
ejpam-3363	251	7	·	·	PUNCT
ejpam-3363	251	8	·	·	PUNCT
ejpam-3363	251	9	·	·	PUNCT
ejpam-3363	252	1	∪dm	∪dm	NOUN
ejpam-3363	252	2	,	,	PUNCT
ejpam-3363	252	3	which	which	PRON
ejpam-3363	252	4	is	be	AUX
ejpam-3363	252	5	a	a	DET
ejpam-3363	252	6	δ	δ	NOUN
ejpam-3363	252	7	-	-	PUNCT
ejpam-3363	252	8	fine	fine	ADJ
ejpam-3363	252	9	belated	belate	VERB
ejpam-3363	252	10	partial	partial	ADJ
ejpam-3363	252	11	division	division	NOUN
ejpam-3363	252	12	of	of	ADP
ejpam-3363	252	13	[	[	X
ejpam-3363	252	14	0	0	NUM
ejpam-3363	252	15	,	,	PUNCT
ejpam-3363	252	16	t	t	X
ejpam-3363	252	17	]	]	PUNCT
ejpam-3363	252	18	with	with	ADP
ejpam-3363	252	19	(	(	PUNCT
ejpam-3363	252	20	p	p	NOUN
ejpam-3363	252	21	)	)	PUNCT
ejpam-3363	252	22	∑	∑	PUNCT
ejpam-3363	252	23	(	(	PUNCT
ejpam-3363	252	24	v	v	ADP
ejpam-3363	252	25	−	−	PROPN
ejpam-3363	252	26	u	u	NOUN
ejpam-3363	252	27	)	)	PUNCT
ejpam-3363	252	28	≤	≤	NOUN
ejpam-3363	252	29	m∑	m∑	SCONJ
ejpam-3363	252	30	j=1	j=1	NOUN
ejpam-3363	252	31	(	(	PUNCT
ejpam-3363	252	32	bj	bj	ADP
ejpam-3363	252	33	−	−	PROPN
ejpam-3363	252	34	aj	aj	PROPN
ejpam-3363	252	35	)	)	PUNCT
ejpam-3363	252	36	≤	≤	PROPN
ejpam-3363	252	37	η	η	PROPN
ejpam-3363	252	38	.	.	PROPN
ejpam-3363	253	1	this	this	PRON
ejpam-3363	253	2	implies	imply	VERB
ejpam-3363	253	3	that	that	SCONJ
ejpam-3363	253	4	e	e	PROPN
ejpam-3363	253	5	[	[	X
ejpam-3363	253	6	∥∥∥(p	∥∥∥(p	PUNCT
ejpam-3363	253	7	)	)	PUNCT
ejpam-3363	253	8	∑	∑	PUNCT
ejpam-3363	253	9	fξ(wv	fξ(wv	NOUN
ejpam-3363	253	10	−wu	−wu	NUM
ejpam-3363	253	11	)	)	PUNCT
ejpam-3363	253	12	∥∥∥2	∥∥∥2	NOUN
ejpam-3363	253	13	v	v	ADP
ejpam-3363	253	14	]	]	PUNCT
ejpam-3363	253	15	<	<	X
ejpam-3363	253	16	ε	ε	PROPN
ejpam-3363	253	17	4	4	NUM
ejpam-3363	253	18	.	.	PUNCT
ejpam-3363	254	1	hence	hence	ADV
ejpam-3363	254	2	,	,	PUNCT
ejpam-3363	254	3	e	e	PROPN
ejpam-3363	254	4	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-3363	254	5	m∑	m∑	ADV
ejpam-3363	254	6	j=1	j=1	PROPN
ejpam-3363	254	7	f	f	PROPN
ejpam-3363	255	1	[	[	X
ejpam-3363	255	2	aj	aj	PROPN
ejpam-3363	255	3	,	,	PUNCT
ejpam-3363	255	4	bj	bj	VERB
ejpam-3363	255	5	]	]	PUNCT
ejpam-3363	255	6	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-3363	255	7	2	2	NUM
ejpam-3363	255	8	v	v	NOUN
ejpam-3363	255	9			NOUN
ejpam-3363	255	10	≤	≤	NOUN
ejpam-3363	255	11	2e	2e	NOUN
ejpam-3363	255	12	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-3363	256	1	m∑	m∑	ADV
ejpam-3363	256	2	j=1	j=1	PROPN
ejpam-3363	256	3	{	{	PUNCT
ejpam-3363	256	4	f	f	PROPN
ejpam-3363	257	1	[	[	X
ejpam-3363	257	2	aj	aj	PROPN
ejpam-3363	257	3	,	,	PUNCT
ejpam-3363	257	4	bj	bj	ADP
ejpam-3363	257	5	]	]	PUNCT
ejpam-3363	257	6	−	−	X
ejpam-3363	257	7	s(f	s(f	NUM
ejpam-3363	257	8	,	,	PUNCT
ejpam-3363	257	9	dj	dj	NOUN
ejpam-3363	257	10	,	,	PUNCT
ejpam-3363	257	11	δj	δj	INTJ
ejpam-3363	257	12	,	,	PUNCT
ejpam-3363	257	13	ηj	ηj	NOUN
ejpam-3363	257	14	)	)	PUNCT
ejpam-3363	257	15	}	}	PUNCT
ejpam-3363	257	16	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-3363	258	1	2	2	NUM
ejpam-3363	258	2	v	v	NOUN
ejpam-3363	258	3			NOUN
ejpam-3363	258	4	+	+	CCONJ
ejpam-3363	258	5	2e	2e	NOUN
ejpam-3363	258	6	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ejpam-3363	258	7	m∑	m∑	ADV
ejpam-3363	258	8	j=1	j=1	PROPN
ejpam-3363	258	9	s(f	s(f	PROPN
ejpam-3363	258	10	,	,	PUNCT
ejpam-3363	258	11	dj	dj	NOUN
ejpam-3363	258	12	,	,	PUNCT
ejpam-3363	258	13	δj	δj	INTJ
ejpam-3363	258	14	,	,	PUNCT
ejpam-3363	258	15	ηj	ηj	NOUN
ejpam-3363	258	16	)	)	PUNCT
ejpam-3363	258	17	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-3363	258	18	2	2	NUM
ejpam-3363	258	19	v	v	NOUN
ejpam-3363	258	20			NOUN
ejpam-3363	258	21	≤	≤	ADV
ejpam-3363	258	22	2	2	NUM
ejpam-3363	258	23			PROPN
ejpam-3363	258	24	m∑	m∑	ADV
ejpam-3363	258	25	j=1	j=1	NOUN
ejpam-3363	258	26	√	√	NUM
ejpam-3363	258	27	e	e	X
ejpam-3363	258	28	[	[	PUNCT
ejpam-3363	258	29	‖f	‖f	ADP
ejpam-3363	258	30	[	[	PUNCT
ejpam-3363	258	31	aj	aj	PROPN
ejpam-3363	258	32	,	,	PUNCT
ejpam-3363	258	33	bj	bj	ADP
ejpam-3363	258	34	]	]	PUNCT
ejpam-3363	258	35	−	−	X
ejpam-3363	258	36	s(f	s(f	NUM
ejpam-3363	258	37	,	,	PUNCT
ejpam-3363	258	38	dj	dj	NOUN
ejpam-3363	258	39	,	,	PUNCT
ejpam-3363	258	40	δj	δj	INTJ
ejpam-3363	258	41	,	,	PUNCT
ejpam-3363	258	42	ηj)‖2v	ηj)‖2v	PROPN
ejpam-3363	258	43	]	]	X
ejpam-3363	258	44	2	2	PROPN
ejpam-3363	258	45	2e	2e	PROPN
ejpam-3363	259	1	[	[	X
ejpam-3363	259	2	∥∥∥(p	∥∥∥(p	PUNCT
ejpam-3363	259	3	)	)	PUNCT
ejpam-3363	259	4	∑	∑	PUNCT
ejpam-3363	259	5	fξ(wv	fξ(wv	NOUN
ejpam-3363	259	6	−wu	−wu	NUM
ejpam-3363	259	7	)	)	PUNCT
ejpam-3363	259	8	∥∥∥2	∥∥∥2	NOUN
ejpam-3363	259	9	v	v	ADP
ejpam-3363	259	10	]	]	PUNCT
ejpam-3363	259	11	<	<	X
ejpam-3363	259	12	2	2	NUM
ejpam-3363	259	13			PROPN
ejpam-3363	259	14	∞∑	∞∑	NUM
ejpam-3363	259	15	j=1	j=1	ADJ
ejpam-3363	259	16	√	√	NUM
ejpam-3363	259	17	ε	ε	PROPN
ejpam-3363	259	18	2	2	NUM
ejpam-3363	259	19	·	·	PUNCT
ejpam-3363	259	20	2j	2j	X
ejpam-3363	259	21	2	2	X
ejpam-3363	260	1	+	+	CCONJ
ejpam-3363	260	2	2	2	NUM
ejpam-3363	260	3	(	(	PUNCT
ejpam-3363	260	4	ε	ε	PROPN
ejpam-3363	260	5	4	4	NUM
ejpam-3363	260	6	)	)	PUNCT
ejpam-3363	260	7	≤	≤	NUM
ejpam-3363	260	8	ε	ε	PROPN
ejpam-3363	260	9	.	.	PUNCT
ejpam-3363	261	1	(	(	PUNCT
ejpam-3363	261	2	7	7	NUM
ejpam-3363	261	3	)	)	PUNCT
ejpam-3363	261	4	thus	thus	ADV
ejpam-3363	261	5	,	,	PUNCT
ejpam-3363	261	6	f	f	PROPN
ejpam-3363	261	7	is	be	AUX
ejpam-3363	261	8	ac2[0	ac2[0	ADJ
ejpam-3363	261	9	,	,	PUNCT
ejpam-3363	261	10	t	t	X
ejpam-3363	261	11	]	]	PUNCT
ejpam-3363	261	12	.	.	PUNCT
ejpam-3363	262	1	conversely	conversely	ADV
ejpam-3363	262	2	,	,	PUNCT
ejpam-3363	262	3	assume	assume	VERB
ejpam-3363	262	4	that	that	SCONJ
ejpam-3363	262	5	(	(	PUNCT
ejpam-3363	262	6	i	i	NOUN
ejpam-3363	262	7	)	)	PUNCT
ejpam-3363	262	8	and	and	CCONJ
ejpam-3363	262	9	(	(	PUNCT
ejpam-3363	262	10	ii	ii	NOUN
ejpam-3363	262	11	)	)	PUNCT
ejpam-3363	262	12	hold	hold	VERB
ejpam-3363	262	13	.	.	PUNCT
ejpam-3363	263	1	let	let	VERB
ejpam-3363	263	2	ε	ε	PROPN
ejpam-3363	263	3	>	>	X
ejpam-3363	263	4	0	0	PUNCT
ejpam-3363	263	5	be	be	AUX
ejpam-3363	263	6	given	give	VERB
ejpam-3363	263	7	.	.	PUNCT
ejpam-3363	264	1	since	since	SCONJ
ejpam-3363	264	2	f	f	PROPN
ejpam-3363	264	3	is	be	AUX
ejpam-3363	264	4	ac2[0	ac2[0	ADJ
ejpam-3363	264	5	,	,	PUNCT
ejpam-3363	264	6	t	t	X
ejpam-3363	264	7	]	]	PUNCT
ejpam-3363	264	8	,	,	PUNCT
ejpam-3363	264	9	choose	choose	VERB
ejpam-3363	264	10	η	η	X
ejpam-3363	264	11	>	>	X
ejpam-3363	264	12	0	0	NUM
ejpam-3363	264	13	such	such	ADJ
ejpam-3363	264	14	that	that	SCONJ
ejpam-3363	264	15	whenever	whenever	SCONJ
ejpam-3363	264	16	{	{	PUNCT
ejpam-3363	264	17	[	[	X
ejpam-3363	264	18	uj	uj	X
ejpam-3363	264	19	,	,	PUNCT
ejpam-3363	264	20	vj	vj	X
ejpam-3363	264	21	]	]	X
ejpam-3363	264	22	}	}	PUNCT
ejpam-3363	264	23	mj=1	mj=1	PRON
ejpam-3363	264	24	is	be	AUX
ejpam-3363	264	25	a	a	DET
ejpam-3363	264	26	finite	finite	ADJ
ejpam-3363	264	27	collection	collection	NOUN
ejpam-3363	264	28	of	of	ADP
ejpam-3363	264	29	subintervals	subinterval	NOUN
ejpam-3363	264	30	[	[	X
ejpam-3363	264	31	uj	uj	X
ejpam-3363	264	32	,	,	PUNCT
ejpam-3363	264	33	vj	vj	INTJ
ejpam-3363	264	34	]	]	PUNCT
ejpam-3363	264	35	∈	∈	PROPN
ejpam-3363	264	36	j	j	PROPN
ejpam-3363	264	37	with	with	ADP
ejpam-3363	264	38	∑m	∑m	PROPN
ejpam-3363	264	39	j=1(vj	j=1(vj	PROPN
ejpam-3363	264	40	−	−	PROPN
ejpam-3363	264	41	uj	uj	PROPN
ejpam-3363	264	42	)	)	PUNCT
ejpam-3363	264	43	≤	≤	PROPN
ejpam-3363	264	44	η	η	PROPN
ejpam-3363	264	45	,	,	PUNCT
ejpam-3363	264	46	we	we	PRON
ejpam-3363	264	47	have	have	VERB
ejpam-3363	264	48	e	e	X
ejpam-3363	264	49	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-3363	264	50	m∑	m∑	ADV
ejpam-3363	264	51	j=1	j=1	PROPN
ejpam-3363	264	52	f	f	PROPN
ejpam-3363	265	1	[	[	X
ejpam-3363	265	2	uj	uj	PROPN
ejpam-3363	265	3	,	,	PUNCT
ejpam-3363	265	4	vj	vj	X
ejpam-3363	265	5	]	]	PUNCT
ejpam-3363	265	6	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-3363	265	7	2	2	NUM
ejpam-3363	265	8	v	v	NOUN
ejpam-3363	265	9			NOUN
ejpam-3363	265	10	<	<	X
ejpam-3363	265	11	ε	ε	PROPN
ejpam-3363	265	12	4	4	NUM
ejpam-3363	265	13	.	.	PUNCT
ejpam-3363	266	1	let	let	VERB
ejpam-3363	266	2	d	d	NOUN
ejpam-3363	266	3	=	=	PRON
ejpam-3363	266	4	{	{	PUNCT
ejpam-3363	266	5	(	(	PUNCT
ejpam-3363	266	6	[	[	X
ejpam-3363	266	7	u	u	NOUN
ejpam-3363	266	8	,	,	PUNCT
ejpam-3363	266	9	v	v	ADP
ejpam-3363	266	10	]	]	X
ejpam-3363	266	11	,	,	PUNCT
ejpam-3363	266	12	ξ	ξ	X
ejpam-3363	266	13	)	)	PUNCT
ejpam-3363	266	14	}	}	PUNCT
ejpam-3363	266	15	be	be	AUX
ejpam-3363	266	16	a	a	DET
ejpam-3363	266	17	(	(	PUNCT
ejpam-3363	266	18	δ	δ	PROPN
ejpam-3363	266	19	,	,	PUNCT
ejpam-3363	266	20	η)-fine	η)-fine	PROPN
ejpam-3363	266	21	belated	belate	VERB
ejpam-3363	266	22	mcshane	mcshane	PROPN
ejpam-3363	266	23	partial	partial	ADJ
ejpam-3363	266	24	division	division	NOUN
ejpam-3363	266	25	of	of	ADP
ejpam-3363	266	26	[	[	X
ejpam-3363	266	27	0	0	NUM
ejpam-3363	266	28	,	,	PUNCT
ejpam-3363	266	29	t	t	NOUN
ejpam-3363	266	30	]	]	PUNCT
ejpam-3363	266	31	and	and	CCONJ
ejpam-3363	266	32	let	let	VERB
ejpam-3363	266	33	dc	dc	PROPN
ejpam-3363	266	34	=	=	PUNCT
ejpam-3363	266	35	{	{	PUNCT
ejpam-3363	266	36	[	[	X
ejpam-3363	266	37	u	u	NOUN
ejpam-3363	266	38	,	,	PUNCT
ejpam-3363	266	39	v	v	ADP
ejpam-3363	266	40	]	]	PUNCT
ejpam-3363	266	41	}	}	PUNCT
ejpam-3363	266	42	be	be	AUX
ejpam-3363	266	43	the	the	DET
ejpam-3363	266	44	collection	collection	NOUN
ejpam-3363	266	45	of	of	ADP
ejpam-3363	266	46	all	all	DET
ejpam-3363	266	47	subintervals	subinterval	NOUN
ejpam-3363	266	48	[	[	X
ejpam-3363	266	49	u	u	NOUN
ejpam-3363	266	50	,	,	PUNCT
ejpam-3363	266	51	v	v	ADP
ejpam-3363	266	52	]	]	X
ejpam-3363	266	53	⊂	⊂	PROPN
ejpam-3363	267	1	[	[	X
ejpam-3363	267	2	0	0	NUM
ejpam-3363	267	3	,	,	PUNCT
ejpam-3363	267	4	t	t	PROPN
ejpam-3363	267	5	]	]	PUNCT
ejpam-3363	267	6	which	which	PRON
ejpam-3363	267	7	are	be	AUX
ejpam-3363	267	8	not	not	PART
ejpam-3363	267	9	included	include	VERB
ejpam-3363	267	10	in	in	ADP
ejpam-3363	267	11	the	the	DET
ejpam-3363	267	12	set	set	NOUN
ejpam-3363	267	13	d.	d.	PROPN
ejpam-3363	267	14	since	since	SCONJ
ejpam-3363	267	15	f	f	PROPN
ejpam-3363	267	16	is	be	AUX
ejpam-3363	267	17	ac2[0	ac2[0	ADJ
ejpam-3363	267	18	,	,	PUNCT
ejpam-3363	267	19	t	t	X
ejpam-3363	267	20	]	]	PUNCT
ejpam-3363	267	21	,	,	PUNCT
ejpam-3363	267	22	e	e	PROPN
ejpam-3363	267	23	[	[	X
ejpam-3363	267	24	∥∥∥(dc	∥∥∥(dc	PROPN
ejpam-3363	267	25	)	)	PUNCT
ejpam-3363	267	26	∑	∑	PUNCT
ejpam-3363	268	1	f	f	PROPN
ejpam-3363	269	1	[	[	X
ejpam-3363	269	2	u	u	NOUN
ejpam-3363	269	3	,	,	PUNCT
ejpam-3363	269	4	v	v	NOUN
ejpam-3363	269	5	]	]	X
ejpam-3363	269	6	∥∥∥2	∥∥∥2	NOUN
ejpam-3363	269	7	v	v	ADP
ejpam-3363	269	8	]	]	PUNCT
ejpam-3363	269	9	<	<	X
ejpam-3363	269	10	ε	ε	PROPN
ejpam-3363	269	11	4	4	NUM
ejpam-3363	269	12	.	.	PUNCT
ejpam-3363	270	1	j.d	j.d	PROPN
ejpam-3363	270	2	.	.	PROPN
ejpam-3363	270	3	cagubcob	cagubcob	PROPN
ejpam-3363	270	4	,	,	PUNCT
ejpam-3363	270	5	m.	m.	NOUN
ejpam-3363	270	6	labendia	labendia	PROPN
ejpam-3363	270	7	/	/	SYM
ejpam-3363	270	8	eur	eur	PROPN
ejpam-3363	270	9	.	.	PUNCT
ejpam-3363	271	1	j.	j.	PROPN
ejpam-3363	271	2	pure	pure	PROPN
ejpam-3363	271	3	appl	appl	PROPN
ejpam-3363	271	4	.	.	PROPN
ejpam-3363	271	5	math	math	PROPN
ejpam-3363	271	6	,	,	PUNCT
ejpam-3363	271	7	12	12	NUM
ejpam-3363	271	8	(	(	PUNCT
ejpam-3363	271	9	1	1	NUM
ejpam-3363	271	10	)	)	PUNCT
ejpam-3363	271	11	(	(	PUNCT
ejpam-3363	271	12	2019	2019	NUM
ejpam-3363	271	13	)	)	PUNCT
ejpam-3363	271	14	,	,	PUNCT
ejpam-3363	271	15	101	101	NUM
ejpam-3363	271	16	-	-	SYM
ejpam-3363	271	17	117	117	NUM
ejpam-3363	271	18	111	111	NUM
ejpam-3363	271	19	hence	hence	ADV
ejpam-3363	271	20	,	,	PUNCT
ejpam-3363	271	21	e	e	X
ejpam-3363	271	22	[	[	X
ejpam-3363	271	23	∥∥∥(d	∥∥∥(d	X
ejpam-3363	271	24	)	)	PUNCT
ejpam-3363	271	25	∑	∑	PUNCT
ejpam-3363	271	26	fξ(wv	fξ(wv	VERB
ejpam-3363	271	27	−wu)−	−wu)−	DET
ejpam-3363	271	28	f	f	PROPN
ejpam-3363	272	1	[	[	X
ejpam-3363	272	2	0	0	NUM
ejpam-3363	272	3	,	,	PUNCT
ejpam-3363	272	4	t	t	X
ejpam-3363	272	5	]	]	PUNCT
ejpam-3363	272	6	∥∥∥2	∥∥∥2	X
ejpam-3363	272	7	v	v	ADP
ejpam-3363	272	8	]	]	PUNCT
ejpam-3363	272	9	≤	≤	NUM
ejpam-3363	272	10	2e	2e	NOUN
ejpam-3363	272	11	[	[	X
ejpam-3363	272	12	∥∥∥(d	∥∥∥(d	X
ejpam-3363	272	13	)	)	PUNCT
ejpam-3363	272	14	∑	∑	PUNCT
ejpam-3363	272	15	{	{	PUNCT
ejpam-3363	272	16	fξ(wv	fξ(wv	VERB
ejpam-3363	272	17	−wu)−	−wu)−	ADP
ejpam-3363	272	18	f	f	NOUN
ejpam-3363	273	1	[	[	X
ejpam-3363	273	2	u	u	NOUN
ejpam-3363	273	3	,	,	PUNCT
ejpam-3363	273	4	v	v	NOUN
ejpam-3363	273	5	]	]	X
ejpam-3363	273	6	}	}	PUNCT
ejpam-3363	273	7	∥∥∥2	∥∥∥2	NOUN
ejpam-3363	273	8	v	v	NOUN
ejpam-3363	273	9	]	]	PUNCT
ejpam-3363	274	1	+	+	CCONJ
ejpam-3363	274	2	2e	2e	NUM
ejpam-3363	274	3	[	[	X
ejpam-3363	274	4	∥∥∥(dc	∥∥∥(dc	PROPN
ejpam-3363	274	5	)	)	PUNCT
ejpam-3363	274	6	∑	∑	PUNCT
ejpam-3363	274	7	f	f	PROPN
ejpam-3363	275	1	[	[	X
ejpam-3363	275	2	u	u	NOUN
ejpam-3363	275	3	,	,	PUNCT
ejpam-3363	275	4	v	v	NOUN
ejpam-3363	275	5	]	]	X
ejpam-3363	275	6	∥∥∥2	∥∥∥2	NOUN
ejpam-3363	275	7	v	v	ADP
ejpam-3363	275	8	]	]	PUNCT
ejpam-3363	275	9	<	<	X
ejpam-3363	275	10	2	2	NUM
ejpam-3363	275	11	(	(	PUNCT
ejpam-3363	275	12	ε	ε	PROPN
ejpam-3363	275	13	4	4	NUM
ejpam-3363	275	14	)	)	PUNCT
ejpam-3363	275	15	+	+	CCONJ
ejpam-3363	275	16	2	2	NUM
ejpam-3363	275	17	(	(	PUNCT
ejpam-3363	275	18	ε	ε	PROPN
ejpam-3363	275	19	4	4	NUM
ejpam-3363	275	20	)	)	PUNCT
ejpam-3363	275	21	=	=	SYM
ejpam-3363	275	22	ε	ε	PROPN
ejpam-3363	275	23	.	.	PUNCT
ejpam-3363	275	24	(	(	PUNCT
ejpam-3363	275	25	8)	8)	NUM
ejpam-3363	275	26	thus	thus	ADV
ejpam-3363	275	27	,	,	PUNCT
ejpam-3363	275	28	f	f	PROPN
ejpam-3363	275	29	is	be	AUX
ejpam-3363	275	30	im	im	ADV
ejpam-3363	275	31	-	-	PUNCT
ejpam-3363	275	32	integrable	integrable	ADJ
ejpam-3363	275	33	to	to	ADP
ejpam-3363	275	34	f	f	PROPN
ejpam-3363	276	1	[	[	X
ejpam-3363	276	2	0	0	NUM
ejpam-3363	276	3	,	,	PUNCT
ejpam-3363	276	4	t	t	X
ejpam-3363	276	5	]	]	PUNCT
ejpam-3363	276	6	.	.	PUNCT
ejpam-3363	277	1	lemma	lemma	PROPN
ejpam-3363	277	2	5	5	X
ejpam-3363	277	3	.	.	PUNCT
ejpam-3363	278	1	let	let	VERB
ejpam-3363	278	2	f	f	PROPN
ejpam-3363	278	3	∈	∈	PROPN
ejpam-3363	278	4	λim	λim	X
ejpam-3363	278	5	and	and	CCONJ
ejpam-3363	278	6	define	define	VERB
ejpam-3363	278	7	f	f	PROPN
ejpam-3363	278	8	:	:	PUNCT
ejpam-3363	278	9	j	j	PROPN
ejpam-3363	278	10	×	×	PROPN
ejpam-3363	278	11	ω→	ω→	NUM
ejpam-3363	278	12	v	v	NOUN
ejpam-3363	278	13	by	by	ADP
ejpam-3363	278	14	f	f	PROPN
ejpam-3363	278	15	[	[	X
ejpam-3363	278	16	u	u	NOUN
ejpam-3363	278	17	,	,	PUNCT
ejpam-3363	278	18	v	v	NOUN
ejpam-3363	278	19	]	]	PUNCT
ejpam-3363	278	20	:	:	PUNCT
ejpam-3363	278	21	=	=	SYM
ejpam-3363	278	22	(	(	PUNCT
ejpam-3363	278	23	i	i	NOUN
ejpam-3363	278	24	m	m	VERB
ejpam-3363	278	25	)	)	PUNCT
ejpam-3363	278	26	∫	∫	PROPN
ejpam-3363	278	27	v	v	NUM
ejpam-3363	278	28	u	u	PROPN
ejpam-3363	278	29	ft	ft	PROPN
ejpam-3363	278	30	dwt	dwt	NOUN
ejpam-3363	278	31	.	.	PUNCT
ejpam-3363	279	1	(	(	PUNCT
ejpam-3363	279	2	i	i	NOUN
ejpam-3363	279	3	)	)	PUNCT
ejpam-3363	279	4	f	f	PROPN
ejpam-3363	279	5	has	have	VERB
ejpam-3363	279	6	the	the	DET
ejpam-3363	279	7	orthogonal	orthogonal	ADJ
ejpam-3363	279	8	increment	increment	NOUN
ejpam-3363	279	9	property	property	NOUN
ejpam-3363	279	10	,	,	PUNCT
ejpam-3363	279	11	(	(	PUNCT
ejpam-3363	279	12	ii	ii	NOUN
ejpam-3363	279	13	)	)	PUNCT
ejpam-3363	279	14	e	e	X
ejpam-3363	280	1	[	[	X
ejpam-3363	280	2	〈	〈	PROPN
ejpam-3363	280	3	fc(wb	fc(wb	NOUN
ejpam-3363	280	4	−wa	−wa	NOUN
ejpam-3363	280	5	)	)	PUNCT
ejpam-3363	280	6	,	,	PUNCT
ejpam-3363	280	7	f	f	PROPN
ejpam-3363	281	1	[	[	X
ejpam-3363	281	2	u	u	NOUN
ejpam-3363	281	3	,	,	PUNCT
ejpam-3363	281	4	v]〉v	v]〉v	NOUN
ejpam-3363	281	5	]	]	X
ejpam-3363	281	6	=	=	SYM
ejpam-3363	281	7	0	0	NUM
ejpam-3363	281	8	,	,	PUNCT
ejpam-3363	281	9	where	where	SCONJ
ejpam-3363	281	10	c	c	NOUN
ejpam-3363	281	11	≤	≤	NOUN
ejpam-3363	281	12	a.	a.	NOUN
ejpam-3363	281	13	proof	proof	NOUN
ejpam-3363	281	14	.	.	PUNCT
ejpam-3363	282	1	we	we	PRON
ejpam-3363	282	2	shall	shall	AUX
ejpam-3363	282	3	only	only	ADV
ejpam-3363	282	4	prove	prove	VERB
ejpam-3363	282	5	(	(	PUNCT
ejpam-3363	282	6	i	i	NOUN
ejpam-3363	282	7	)	)	PUNCT
ejpam-3363	282	8	since	since	SCONJ
ejpam-3363	282	9	(	(	PUNCT
ejpam-3363	282	10	ii	ii	NOUN
ejpam-3363	282	11	)	)	PUNCT
ejpam-3363	282	12	follows	follow	VERB
ejpam-3363	282	13	the	the	DET
ejpam-3363	282	14	same	same	ADJ
ejpam-3363	282	15	arguments	argument	NOUN
ejpam-3363	282	16	in	in	ADP
ejpam-3363	282	17	(	(	PUNCT
ejpam-3363	282	18	i	i	NOUN
ejpam-3363	282	19	)	)	PUNCT
ejpam-3363	282	20	.	.	PUNCT
ejpam-3363	283	1	by	by	ADP
ejpam-3363	283	2	the	the	DET
ejpam-3363	283	3	sequential	sequential	ADJ
ejpam-3363	283	4	definition	definition	NOUN
ejpam-3363	283	5	of	of	ADP
ejpam-3363	283	6	i	i	PRON
ejpam-3363	283	7	m	m	VERB
ejpam-3363	283	8	integral	integral	ADJ
ejpam-3363	283	9	,	,	PUNCT
ejpam-3363	283	10	there	there	PRON
ejpam-3363	283	11	exists	exist	VERB
ejpam-3363	283	12	a	a	DET
ejpam-3363	283	13	decreasing	decrease	VERB
ejpam-3363	283	14	sequence	sequence	NOUN
ejpam-3363	283	15	{	{	PUNCT
ejpam-3363	283	16	δn	δn	NOUN
ejpam-3363	283	17	}	}	PUNCT
ejpam-3363	283	18	of	of	ADP
ejpam-3363	283	19	positive	positive	ADJ
ejpam-3363	283	20	functions	function	NOUN
ejpam-3363	283	21	defined	define	VERB
ejpam-3363	283	22	on	on	ADP
ejpam-3363	283	23	[	[	X
ejpam-3363	283	24	0	0	NUM
ejpam-3363	283	25	,	,	PUNCT
ejpam-3363	283	26	t	t	NOUN
ejpam-3363	283	27	]	]	PUNCT
ejpam-3363	283	28	and	and	CCONJ
ejpam-3363	283	29	a	a	DET
ejpam-3363	283	30	decreasing	decrease	VERB
ejpam-3363	283	31	sequence	sequence	NOUN
ejpam-3363	283	32	{	{	PUNCT
ejpam-3363	283	33	ηn	ηn	ADJ
ejpam-3363	283	34	}	}	PUNCT
ejpam-3363	283	35	of	of	ADP
ejpam-3363	283	36	positive	positive	ADJ
ejpam-3363	283	37	numbers	number	NOUN
ejpam-3363	283	38	such	such	ADJ
ejpam-3363	283	39	that	that	PRON
ejpam-3363	283	40	for	for	ADP
ejpam-3363	283	41	any	any	DET
ejpam-3363	283	42	(	(	PUNCT
ejpam-3363	283	43	δn	δn	NOUN
ejpam-3363	283	44	,	,	PUNCT
ejpam-3363	283	45	ηn)-fine	ηn)-fine	PROPN
ejpam-3363	283	46	belated	belate	VERB
ejpam-3363	283	47	mcshane	mcshane	PROPN
ejpam-3363	283	48	partial	partial	ADJ
ejpam-3363	283	49	division	division	NOUN
ejpam-3363	283	50	dn[a	dn[a	PROPN
ejpam-3363	283	51	,	,	PUNCT
ejpam-3363	283	52	b	b	X
ejpam-3363	283	53	]	]	X
ejpam-3363	283	54	=	=	X
ejpam-3363	283	55	{	{	PUNCT
ejpam-3363	283	56	(	(	PUNCT
ejpam-3363	283	57	[	[	X
ejpam-3363	283	58	u(n)i	u(n)i	PROPN
ejpam-3363	283	59	,	,	PUNCT
ejpam-3363	283	60	v	v	NOUN
ejpam-3363	283	61	(	(	PUNCT
ejpam-3363	283	62	n	n	CCONJ
ejpam-3363	283	63	)	)	PUNCT
ejpam-3363	283	64	i	i	PRON
ejpam-3363	283	65	,	,	PUNCT
ejpam-3363	283	66	ξ	ξ	PROPN
ejpam-3363	283	67	(	(	PUNCT
ejpam-3363	283	68	n	n	CCONJ
ejpam-3363	283	69	)	)	PUNCT
ejpam-3363	283	70	i	i	PRON
ejpam-3363	283	71	]	]	X
ejpam-3363	283	72	)	)	PUNCT
ejpam-3363	283	73	}	}	PUNCT
ejpam-3363	283	74	mi=1	mi=1	PROPN
ejpam-3363	283	75	and	and	CCONJ
ejpam-3363	283	76	dn[u	dn[u	PROPN
ejpam-3363	283	77	,	,	PUNCT
ejpam-3363	283	78	v	v	NOUN
ejpam-3363	283	79	]	]	X
ejpam-3363	283	80	=	=	PUNCT
ejpam-3363	283	81	{	{	PUNCT
ejpam-3363	283	82	(	(	PUNCT
ejpam-3363	283	83	[	[	X
ejpam-3363	283	84	u(n)j	u(n)j	PROPN
ejpam-3363	283	85	,	,	PUNCT
ejpam-3363	283	86	v	v	NOUN
ejpam-3363	283	87	(	(	PUNCT
ejpam-3363	283	88	n	n	CCONJ
ejpam-3363	283	89	)	)	PUNCT
ejpam-3363	283	90	j	j	PROPN
ejpam-3363	283	91	,	,	PUNCT
ejpam-3363	283	92	ξ	ξ	PROPN
ejpam-3363	283	93	(	(	PUNCT
ejpam-3363	283	94	n	n	CCONJ
ejpam-3363	283	95	)	)	PUNCT
ejpam-3363	283	96	j	j	NOUN
ejpam-3363	283	97	]	]	X
ejpam-3363	283	98	)	)	PUNCT
ejpam-3363	283	99	}	}	PUNCT
ejpam-3363	283	100	pj=1	pj=1	NOUN
ejpam-3363	283	101	of	of	ADP
ejpam-3363	283	102	[	[	X
ejpam-3363	283	103	a	a	X
ejpam-3363	283	104	,	,	PUNCT
ejpam-3363	283	105	b	b	NOUN
ejpam-3363	283	106	]	]	PUNCT
ejpam-3363	283	107	and	and	CCONJ
ejpam-3363	283	108	[	[	X
ejpam-3363	283	109	u	u	NOUN
ejpam-3363	283	110	,	,	PUNCT
ejpam-3363	283	111	v	v	ADP
ejpam-3363	283	112	]	]	X
ejpam-3363	283	113	,	,	PUNCT
ejpam-3363	283	114	respectively	respectively	ADV
ejpam-3363	283	115	,	,	PUNCT
ejpam-3363	283	116	we	we	PRON
ejpam-3363	283	117	have	have	VERB
ejpam-3363	283	118	e	e	X
ejpam-3363	283	119	[	[	PUNCT
ejpam-3363	283	120	‖s(f	‖s(f	ADJ
ejpam-3363	283	121	,	,	PUNCT
ejpam-3363	283	122	dn[a	dn[a	PROPN
ejpam-3363	283	123	,	,	PUNCT
ejpam-3363	283	124	b	b	NOUN
ejpam-3363	283	125	]	]	X
ejpam-3363	283	126	,	,	PUNCT
ejpam-3363	283	127	δn	δn	INTJ
ejpam-3363	283	128	,	,	PUNCT
ejpam-3363	283	129	ηn)−	ηn)−	NOUN
ejpam-3363	284	1	f	f	NOUN
ejpam-3363	285	1	[	[	X
ejpam-3363	285	2	a	a	X
ejpam-3363	285	3	,	,	PUNCT
ejpam-3363	285	4	b]‖2v	b]‖2v	X
ejpam-3363	285	5	]	]	PUNCT
ejpam-3363	285	6	→	→	SYM
ejpam-3363	285	7	0	0	NUM
ejpam-3363	285	8	as	as	ADP
ejpam-3363	285	9	n→∞	n→∞	NUM
ejpam-3363	285	10	and	and	CCONJ
ejpam-3363	285	11	e	e	X
ejpam-3363	285	12	[	[	PUNCT
ejpam-3363	285	13	‖s(f	‖s(f	ADJ
ejpam-3363	285	14	,	,	PUNCT
ejpam-3363	285	15	dn[u	dn[u	PROPN
ejpam-3363	285	16	,	,	PUNCT
ejpam-3363	285	17	v	v	ADP
ejpam-3363	285	18	]	]	X
ejpam-3363	285	19	,	,	PUNCT
ejpam-3363	285	20	δn	δn	INTJ
ejpam-3363	285	21	,	,	PUNCT
ejpam-3363	285	22	ηn)−	ηn)−	NOUN
ejpam-3363	285	23	f	f	X
ejpam-3363	286	1	[	[	X
ejpam-3363	286	2	u	u	NOUN
ejpam-3363	286	3	,	,	PUNCT
ejpam-3363	286	4	v]‖2v	v]‖2v	NOUN
ejpam-3363	286	5	]	]	PUNCT
ejpam-3363	286	6	→	→	SYM
ejpam-3363	286	7	0	0	NUM
ejpam-3363	286	8	as	as	ADP
ejpam-3363	286	9	n→∞.	n→∞.	VERB
ejpam-3363	286	10	by	by	ADP
ejpam-3363	286	11	lemma	lemma	PROPN
ejpam-3363	286	12	2	2	NUM
ejpam-3363	286	13	,	,	PUNCT
ejpam-3363	286	14	for	for	ADP
ejpam-3363	286	15	every	every	DET
ejpam-3363	286	16	n	n	CCONJ
ejpam-3363	286	17	∈	∈	PROPN
ejpam-3363	286	18	n	n	PRON
ejpam-3363	286	19	e	e	NOUN
ejpam-3363	286	20			NOUN
ejpam-3363	286	21	m∑	m∑	VERB
ejpam-3363	286	22	i=1	i=1	PROPN
ejpam-3363	286	23	p∑	p∑	PROPN
ejpam-3363	287	1	j=1	j=1	PROPN
ejpam-3363	287	2	〈	〈	PROPN
ejpam-3363	287	3	fξi(n)(w	fξi(n)(w	NOUN
ejpam-3363	287	4	v	v	NOUN
ejpam-3363	287	5	(	(	PUNCT
ejpam-3363	287	6	n	n	CCONJ
ejpam-3363	287	7	)	)	PUNCT
ejpam-3363	287	8	i	i	PRON
ejpam-3363	287	9	−w	−w	ADV
ejpam-3363	287	10	u	u	NOUN
ejpam-3363	287	11	(	(	PUNCT
ejpam-3363	287	12	n	n	CCONJ
ejpam-3363	287	13	)	)	PUNCT
ejpam-3363	287	14	i	i	PRON
ejpam-3363	287	15	)	)	PUNCT
ejpam-3363	287	16	,	,	PUNCT
ejpam-3363	287	17	f	f	PROPN
ejpam-3363	287	18	ξ	ξ	PROPN
ejpam-3363	287	19	(	(	PUNCT
ejpam-3363	287	20	n	n	CCONJ
ejpam-3363	287	21	)	)	PUNCT
ejpam-3363	287	22	j	j	PROPN
ejpam-3363	287	23	(	(	PUNCT
ejpam-3363	287	24	w	w	NOUN
ejpam-3363	287	25	v	v	PROPN
ejpam-3363	287	26	(	(	PUNCT
ejpam-3363	287	27	n	n	CCONJ
ejpam-3363	287	28	)	)	PUNCT
ejpam-3363	287	29	j	j	PROPN
ejpam-3363	288	1	−w	−w	ADV
ejpam-3363	288	2	u	u	PROPN
ejpam-3363	288	3	(	(	PUNCT
ejpam-3363	288	4	n	n	CCONJ
ejpam-3363	288	5	)	)	PUNCT
ejpam-3363	288	6	j	j	NOUN
ejpam-3363	288	7	)	)	PUNCT
ejpam-3363	288	8	〉	〉	NOUN
ejpam-3363	288	9	v	v	ADP
ejpam-3363	288	10			NOUN
ejpam-3363	288	11	=	=	SYM
ejpam-3363	288	12	0	0	X
ejpam-3363	288	13	.	.	PUNCT
ejpam-3363	289	1	since	since	SCONJ
ejpam-3363	289	2	s(f	s(f	PROPN
ejpam-3363	289	3	,	,	PUNCT
ejpam-3363	289	4	dn[a	dn[a	PROPN
ejpam-3363	289	5	,	,	PUNCT
ejpam-3363	289	6	b	b	NOUN
ejpam-3363	289	7	]	]	X
ejpam-3363	289	8	,	,	PUNCT
ejpam-3363	289	9	δn	δn	NOUN
ejpam-3363	289	10	,	,	PUNCT
ejpam-3363	289	11	ηm	ηm	NOUN
ejpam-3363	289	12	)	)	PUNCT
ejpam-3363	289	13	→	→	SYM
ejpam-3363	289	14	f	f	X
ejpam-3363	290	1	[	[	X
ejpam-3363	290	2	a	a	X
ejpam-3363	290	3	,	,	PUNCT
ejpam-3363	290	4	b	b	NOUN
ejpam-3363	290	5	]	]	PUNCT
ejpam-3363	290	6	and	and	CCONJ
ejpam-3363	290	7	s(f	s(f	PROPN
ejpam-3363	290	8	,	,	PUNCT
ejpam-3363	290	9	dn[u	dn[u	PROPN
ejpam-3363	290	10	,	,	PUNCT
ejpam-3363	290	11	v	v	ADP
ejpam-3363	290	12	]	]	X
ejpam-3363	290	13	,	,	PUNCT
ejpam-3363	290	14	δn	δn	NOUN
ejpam-3363	290	15	,	,	PUNCT
ejpam-3363	290	16	ηm	ηm	NOUN
ejpam-3363	290	17	)	)	PUNCT
ejpam-3363	290	18	→	→	SYM
ejpam-3363	290	19	f	f	X
ejpam-3363	291	1	[	[	X
ejpam-3363	291	2	u	u	NOUN
ejpam-3363	291	3	,	,	PUNCT
ejpam-3363	291	4	v	v	ADP
ejpam-3363	291	5	]	]	PUNCT
ejpam-3363	291	6	in	in	ADP
ejpam-3363	291	7	l2(ω	l2(ω	PROPN
ejpam-3363	291	8	,	,	PUNCT
ejpam-3363	291	9	v	v	NOUN
ejpam-3363	291	10	)	)	PUNCT
ejpam-3363	291	11	as	as	ADP
ejpam-3363	291	12	n→∞	n→∞	NUM
ejpam-3363	291	13	,	,	PUNCT
ejpam-3363	291	14	it	it	PRON
ejpam-3363	291	15	follows	follow	VERB
ejpam-3363	291	16	that	that	SCONJ
ejpam-3363	291	17	e	e	PROPN
ejpam-3363	291	18	[	[	X
ejpam-3363	291	19	〈	〈	PROPN
ejpam-3363	291	20	s(f	s(f	PROPN
ejpam-3363	291	21	,	,	PUNCT
ejpam-3363	291	22	dn[a	dn[a	PROPN
ejpam-3363	291	23	,	,	PUNCT
ejpam-3363	291	24	b	b	NOUN
ejpam-3363	291	25	]	]	X
ejpam-3363	291	26	,	,	PUNCT
ejpam-3363	291	27	δn	δn	NOUN
ejpam-3363	291	28	,	,	PUNCT
ejpam-3363	291	29	ηm	ηm	NOUN
ejpam-3363	291	30	)	)	PUNCT
ejpam-3363	291	31	,	,	PUNCT
ejpam-3363	291	32	s(f	s(f	PROPN
ejpam-3363	291	33	,	,	PUNCT
ejpam-3363	291	34	dn[u	dn[u	PROPN
ejpam-3363	291	35	,	,	PUNCT
ejpam-3363	291	36	v	v	ADP
ejpam-3363	291	37	]	]	X
ejpam-3363	291	38	,	,	PUNCT
ejpam-3363	291	39	δn	δn	NOUN
ejpam-3363	291	40	,	,	PUNCT
ejpam-3363	291	41	ηn)〉v	ηn)〉v	PROPN
ejpam-3363	291	42	]	]	PUNCT
ejpam-3363	291	43	→	→	SYM
ejpam-3363	291	44	e	e	X
ejpam-3363	291	45	[	[	X
ejpam-3363	291	46	〈	〈	PROPN
ejpam-3363	291	47	f	f	X
ejpam-3363	291	48	[	[	X
ejpam-3363	291	49	a	a	X
ejpam-3363	291	50	,	,	PUNCT
ejpam-3363	291	51	b	b	NOUN
ejpam-3363	291	52	]	]	X
ejpam-3363	291	53	,	,	PUNCT
ejpam-3363	291	54	f	f	PROPN
ejpam-3363	292	1	[	[	X
ejpam-3363	292	2	u	u	NOUN
ejpam-3363	292	3	,	,	PUNCT
ejpam-3363	292	4	v]〉v	v]〉v	NOUN
ejpam-3363	292	5	]	]	PUNCT
ejpam-3363	292	6	as	as	ADP
ejpam-3363	292	7	n→∞.	n→∞.	PROPN
ejpam-3363	292	8	thus	thus	ADV
ejpam-3363	292	9	,	,	PUNCT
ejpam-3363	292	10	e	e	X
ejpam-3363	293	1	[	[	X
ejpam-3363	293	2	〈	〈	PROPN
ejpam-3363	293	3	f	f	X
ejpam-3363	293	4	[	[	X
ejpam-3363	293	5	a	a	X
ejpam-3363	293	6	,	,	PUNCT
ejpam-3363	293	7	b	b	NOUN
ejpam-3363	293	8	]	]	X
ejpam-3363	293	9	,	,	PUNCT
ejpam-3363	293	10	f	f	PROPN
ejpam-3363	294	1	[	[	X
ejpam-3363	294	2	u	u	NOUN
ejpam-3363	294	3	,	,	PUNCT
ejpam-3363	294	4	v]〉v	v]〉v	NOUN
ejpam-3363	294	5	]	]	X
ejpam-3363	294	6	=	=	SYM
ejpam-3363	294	7	0	0	X
ejpam-3363	294	8	.	.	PUNCT
ejpam-3363	295	1	in	in	ADP
ejpam-3363	295	2	view	view	NOUN
ejpam-3363	295	3	of	of	ADP
ejpam-3363	295	4	lemma	lemma	PROPN
ejpam-3363	295	5	5	5	NUM
ejpam-3363	295	6	,	,	PUNCT
ejpam-3363	295	7	we	we	PRON
ejpam-3363	295	8	have	have	VERB
ejpam-3363	295	9	the	the	DET
ejpam-3363	295	10	following	follow	VERB
ejpam-3363	295	11	lemma	lemma	PROPN
ejpam-3363	295	12	.	.	PUNCT
ejpam-3363	295	13	j.d	j.d	PROPN
ejpam-3363	295	14	.	.	PROPN
ejpam-3363	295	15	cagubcob	cagubcob	PROPN
ejpam-3363	295	16	,	,	PUNCT
ejpam-3363	295	17	m.	m.	NOUN
ejpam-3363	295	18	labendia	labendia	PROPN
ejpam-3363	295	19	/	/	SYM
ejpam-3363	295	20	eur	eur	PROPN
ejpam-3363	295	21	.	.	PUNCT
ejpam-3363	296	1	j.	j.	PROPN
ejpam-3363	296	2	pure	pure	PROPN
ejpam-3363	296	3	appl	appl	PROPN
ejpam-3363	296	4	.	.	PROPN
ejpam-3363	296	5	math	math	PROPN
ejpam-3363	296	6	,	,	PUNCT
ejpam-3363	296	7	12	12	NUM
ejpam-3363	296	8	(	(	PUNCT
ejpam-3363	296	9	1	1	NUM
ejpam-3363	296	10	)	)	PUNCT
ejpam-3363	296	11	(	(	PUNCT
ejpam-3363	296	12	2019	2019	NUM
ejpam-3363	296	13	)	)	PUNCT
ejpam-3363	296	14	,	,	PUNCT
ejpam-3363	296	15	101	101	NUM
ejpam-3363	296	16	-	-	SYM
ejpam-3363	296	17	117	117	NUM
ejpam-3363	296	18	112	112	NUM
ejpam-3363	296	19	lemma	lemma	PROPN
ejpam-3363	296	20	6	6	NUM
ejpam-3363	296	21	.	.	PUNCT
ejpam-3363	297	1	let	let	VERB
ejpam-3363	297	2	f	f	PROPN
ejpam-3363	297	3	∈	∈	PROPN
ejpam-3363	297	4	λim	λim	X
ejpam-3363	297	5	and	and	CCONJ
ejpam-3363	297	6	define	define	VERB
ejpam-3363	297	7	f	f	PROPN
ejpam-3363	297	8	:	:	PUNCT
ejpam-3363	297	9	j	j	PROPN
ejpam-3363	297	10	×	×	PROPN
ejpam-3363	297	11	ω→	ω→	NUM
ejpam-3363	297	12	v	v	NOUN
ejpam-3363	297	13	by	by	ADP
ejpam-3363	297	14	f	f	PROPN
ejpam-3363	297	15	[	[	X
ejpam-3363	297	16	u	u	NOUN
ejpam-3363	297	17	,	,	PUNCT
ejpam-3363	297	18	v	v	NOUN
ejpam-3363	297	19	]	]	PUNCT
ejpam-3363	297	20	:	:	PUNCT
ejpam-3363	297	21	=	=	SYM
ejpam-3363	297	22	(	(	PUNCT
ejpam-3363	297	23	i	i	NOUN
ejpam-3363	297	24	m	m	VERB
ejpam-3363	297	25	)	)	PUNCT
ejpam-3363	297	26	∫	∫	PROPN
ejpam-3363	297	27	v	v	NUM
ejpam-3363	297	28	u	u	PROPN
ejpam-3363	297	29	ft	ft	PROPN
ejpam-3363	297	30	dwt	dwt	NOUN
ejpam-3363	297	31	.	.	PUNCT
ejpam-3363	298	1	let	let	VERB
ejpam-3363	298	2	{	{	PUNCT
ejpam-3363	298	3	(	(	PUNCT
ejpam-3363	298	4	[	[	X
ejpam-3363	298	5	ui	ui	PROPN
ejpam-3363	298	6	,	,	PUNCT
ejpam-3363	298	7	vi	vi	PROPN
ejpam-3363	298	8	]	]	PUNCT
ejpam-3363	298	9	,	,	PUNCT
ejpam-3363	298	10	ξi)}ni=1	ξi)}ni=1	PROPN
ejpam-3363	298	11	be	be	VERB
ejpam-3363	298	12	a	a	DET
ejpam-3363	298	13	finite	finite	ADJ
ejpam-3363	298	14	collection	collection	NOUN
ejpam-3363	298	15	such	such	ADJ
ejpam-3363	298	16	that	that	SCONJ
ejpam-3363	298	17	{	{	PUNCT
ejpam-3363	298	18	[	[	X
ejpam-3363	298	19	ui	ui	NOUN
ejpam-3363	298	20	,	,	PUNCT
ejpam-3363	298	21	vi	vi	PROPN
ejpam-3363	298	22	]	]	PUNCT
ejpam-3363	298	23	}	}	PUNCT
ejpam-3363	298	24	is	be	AUX
ejpam-3363	298	25	a	a	DET
ejpam-3363	298	26	collection	collection	NOUN
ejpam-3363	298	27	of	of	ADP
ejpam-3363	298	28	non	non	ADJ
ejpam-3363	298	29	-	-	ADJ
ejpam-3363	298	30	overlapping	overlapping	ADJ
ejpam-3363	298	31	intervals	interval	NOUN
ejpam-3363	298	32	in	in	ADP
ejpam-3363	298	33	j	j	PROPN
ejpam-3363	298	34	,	,	PUNCT
ejpam-3363	298	35	ξ1	ξ1	PROPN
ejpam-3363	298	36	<	<	X
ejpam-3363	298	37	ξ2	ξ2	NOUN
ejpam-3363	298	38	<	<	X
ejpam-3363	298	39	·	·	PUNCT
ejpam-3363	298	40	·	·	PUNCT
ejpam-3363	298	41	·	·	PUNCT
ejpam-3363	299	1	<	<	X
ejpam-3363	299	2	ξn	ξn	PROPN
ejpam-3363	299	3	,	,	PUNCT
ejpam-3363	299	4	and	and	CCONJ
ejpam-3363	299	5	ξi	ξi	NUM
ejpam-3363	299	6	≤	≤	NUM
ejpam-3363	299	7	ui	ui	NOUN
ejpam-3363	299	8	for	for	ADP
ejpam-3363	299	9	each	each	DET
ejpam-3363	299	10	i	i	NOUN
ejpam-3363	299	11	=	=	NOUN
ejpam-3363	299	12	1	1	NUM
ejpam-3363	299	13	,	,	PUNCT
ejpam-3363	299	14	2	2	NUM
ejpam-3363	299	15	,	,	PUNCT
ejpam-3363	299	16	.	.	PUNCT
ejpam-3363	299	17	.	.	PUNCT
ejpam-3363	299	18	.	.	PUNCT
ejpam-3363	300	1	,	,	PUNCT
ejpam-3363	300	2	n.	n.	PROPN
ejpam-3363	300	3	then	then	ADV
ejpam-3363	300	4	(	(	PUNCT
ejpam-3363	300	5	i	i	NOUN
ejpam-3363	300	6	)	)	PUNCT
ejpam-3363	300	7	e	e	PROPN
ejpam-3363	301	1	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-3363	301	2	n∑	n∑	X
ejpam-3363	301	3	i=1	i=1	PROPN
ejpam-3363	301	4	{	{	PUNCT
ejpam-3363	301	5	fξi(wvi	fξi(wvi	NOUN
ejpam-3363	301	6	−wui)−	−wui)−	PROPN
ejpam-3363	301	7	f	f	PROPN
ejpam-3363	301	8	(	(	PUNCT
ejpam-3363	301	9	ui	ui	PROPN
ejpam-3363	301	10	,	,	PUNCT
ejpam-3363	301	11	vi	vi	NOUN
ejpam-3363	301	12	)	)	PUNCT
ejpam-3363	301	13	}	}	PUNCT
ejpam-3363	301	14	∥∥∥∥∥	∥∥∥∥∥	VERB
ejpam-3363	301	15	2	2	NUM
ejpam-3363	301	16	v	v	NOUN
ejpam-3363	301	17			NOUN
ejpam-3363	301	18	=	=	PUNCT
ejpam-3363	302	1	n∑	n∑	NOUN
ejpam-3363	302	2	i=1	i=1	PROPN
ejpam-3363	303	1	e	e	X
ejpam-3363	303	2	[	[	PUNCT
ejpam-3363	303	3	‖fξi(wvi	‖fξi(wvi	X
ejpam-3363	303	4	−wui)−	−wui)−	PROPN
ejpam-3363	303	5	f	f	X
ejpam-3363	303	6	(	(	PUNCT
ejpam-3363	303	7	ui	ui	PROPN
ejpam-3363	303	8	,	,	PUNCT
ejpam-3363	303	9	vi)‖2v	vi)‖2v	X
ejpam-3363	303	10	]	]	PUNCT
ejpam-3363	303	11	;	;	PUNCT
ejpam-3363	303	12	(	(	PUNCT
ejpam-3363	303	13	ii	ii	NOUN
ejpam-3363	303	14	)	)	PUNCT
ejpam-3363	303	15	e	e	PROPN
ejpam-3363	303	16	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-3363	303	17	n∑	n∑	PROPN
ejpam-3363	303	18	i=1	i=1	PROPN
ejpam-3363	304	1	f	f	PROPN
ejpam-3363	304	2	(	(	PUNCT
ejpam-3363	304	3	ui	ui	PROPN
ejpam-3363	304	4	,	,	PUNCT
ejpam-3363	304	5	vi	vi	PROPN
ejpam-3363	304	6	)	)	PUNCT
ejpam-3363	304	7	∥∥∥∥∥	∥∥∥∥∥	NUM
ejpam-3363	304	8	2	2	NUM
ejpam-3363	304	9	v	v	NOUN
ejpam-3363	304	10			NOUN
ejpam-3363	304	11	=	=	PUNCT
ejpam-3363	304	12	n∑	n∑	NOUN
ejpam-3363	304	13	i=1	i=1	PROPN
ejpam-3363	305	1	e	e	X
ejpam-3363	305	2	[	[	PUNCT
ejpam-3363	305	3	‖f	‖f	ADJ
ejpam-3363	305	4	(	(	PUNCT
ejpam-3363	305	5	ui	ui	PROPN
ejpam-3363	305	6	,	,	PUNCT
ejpam-3363	305	7	vi)‖2v	vi)‖2v	X
ejpam-3363	305	8	]	]	PUNCT
ejpam-3363	305	9	.	.	PUNCT
ejpam-3363	306	1	the	the	DET
ejpam-3363	306	2	immediate	immediate	ADJ
ejpam-3363	306	3	consequence	consequence	NOUN
ejpam-3363	306	4	of	of	ADP
ejpam-3363	306	5	lemma	lemma	PROPN
ejpam-3363	306	6	5.(i	5.(i	NUM
ejpam-3363	306	7	)	)	PUNCT
ejpam-3363	306	8	is	be	AUX
ejpam-3363	306	9	the	the	DET
ejpam-3363	306	10	strong	strong	ADJ
ejpam-3363	306	11	version	version	NOUN
ejpam-3363	306	12	of	of	ADP
ejpam-3363	306	13	saks	sak	NOUN
ejpam-3363	306	14	-	-	PUNCT
ejpam-3363	306	15	henstock	henstock	NUM
ejpam-3363	306	16	lemma	lemma	PROPN
ejpam-3363	306	17	.	.	PUNCT
ejpam-3363	307	1	lemma	lemma	PROPN
ejpam-3363	307	2	7	7	NUM
ejpam-3363	307	3	.	.	PUNCT
ejpam-3363	308	1	(	(	PUNCT
ejpam-3363	308	2	saks	sak	NOUN
ejpam-3363	308	3	-	-	PUNCT
ejpam-3363	308	4	henstock	henstock	NOUN
ejpam-3363	308	5	lemma	lemma	PROPN
ejpam-3363	308	6	(	(	PUNCT
ejpam-3363	308	7	strong	strong	ADJ
ejpam-3363	308	8	version	version	NOUN
ejpam-3363	308	9	)	)	PUNCT
ejpam-3363	308	10	)	)	PUNCT
ejpam-3363	308	11	.	.	PUNCT
ejpam-3363	309	1	let	let	VERB
ejpam-3363	309	2	f	f	PROPN
ejpam-3363	309	3	∈	∈	PROPN
ejpam-3363	309	4	λim	λim	X
ejpam-3363	309	5	and	and	CCONJ
ejpam-3363	309	6	let	let	VERB
ejpam-3363	309	7	f	f	PRON
ejpam-3363	309	8	:	:	PUNCT
ejpam-3363	309	9	j	j	PROPN
ejpam-3363	309	10	×	×	PROPN
ejpam-3363	309	11	ω	ω	PROPN
ejpam-3363	309	12	→	→	SYM
ejpam-3363	309	13	v	v	NUM
ejpam-3363	309	14	be	be	AUX
ejpam-3363	309	15	defined	define	VERB
ejpam-3363	309	16	by	by	ADP
ejpam-3363	309	17	f	f	PROPN
ejpam-3363	309	18	(	(	PUNCT
ejpam-3363	309	19	u	u	NOUN
ejpam-3363	309	20	,	,	PUNCT
ejpam-3363	309	21	v	v	NOUN
ejpam-3363	309	22	)	)	PUNCT
ejpam-3363	309	23	:	:	PUNCT
ejpam-3363	310	1	=	=	SYM
ejpam-3363	310	2	(	(	PUNCT
ejpam-3363	310	3	i	i	NOUN
ejpam-3363	310	4	m	m	VERB
ejpam-3363	310	5	)	)	PUNCT
ejpam-3363	310	6	∫	∫	PROPN
ejpam-3363	310	7	v	v	NUM
ejpam-3363	310	8	u	u	PROPN
ejpam-3363	310	9	ft	ft	PROPN
ejpam-3363	310	10	dwt	dwt	NOUN
ejpam-3363	310	11	.	.	PUNCT
ejpam-3363	311	1	then	then	ADV
ejpam-3363	311	2	for	for	ADP
ejpam-3363	311	3	every	every	DET
ejpam-3363	311	4	ε	ε	PROPN
ejpam-3363	311	5	>	>	X
ejpam-3363	311	6	0	0	PROPN
ejpam-3363	311	7	,	,	PUNCT
ejpam-3363	311	8	there	there	PRON
ejpam-3363	311	9	exists	exist	VERB
ejpam-3363	311	10	a	a	DET
ejpam-3363	311	11	positive	positive	ADJ
ejpam-3363	311	12	function	function	NOUN
ejpam-3363	311	13	δ	δ	PROPN
ejpam-3363	311	14	on	on	ADP
ejpam-3363	311	15	[	[	X
ejpam-3363	311	16	0	0	NUM
ejpam-3363	311	17	,	,	PUNCT
ejpam-3363	311	18	t	t	X
ejpam-3363	311	19	]	]	PUNCT
ejpam-3363	311	20	such	such	ADJ
ejpam-3363	311	21	that	that	PRON
ejpam-3363	311	22	for	for	SCONJ
ejpam-3363	311	23	any	any	DET
ejpam-3363	311	24	δ	δ	NOUN
ejpam-3363	311	25	-	-	PUNCT
ejpam-3363	311	26	fine	fine	NOUN
ejpam-3363	311	27	belated	belate	VERB
ejpam-3363	311	28	mcshane	mcshane	PROPN
ejpam-3363	311	29	partial	partial	ADJ
ejpam-3363	311	30	division	division	NOUN
ejpam-3363	311	31	d	d	NOUN
ejpam-3363	311	32	=	=	PRON
ejpam-3363	311	33	{	{	PUNCT
ejpam-3363	311	34	(	(	PUNCT
ejpam-3363	311	35	[	[	X
ejpam-3363	311	36	u	u	NOUN
ejpam-3363	311	37	,	,	PUNCT
ejpam-3363	311	38	v	v	ADP
ejpam-3363	311	39	]	]	X
ejpam-3363	311	40	,	,	PUNCT
ejpam-3363	311	41	ξ	ξ	X
ejpam-3363	311	42	)	)	PUNCT
ejpam-3363	311	43	}	}	PUNCT
ejpam-3363	311	44	of	of	ADP
ejpam-3363	311	45	[	[	X
ejpam-3363	311	46	0	0	NUM
ejpam-3363	311	47	,	,	PUNCT
ejpam-3363	311	48	t	t	X
ejpam-3363	311	49	]	]	PUNCT
ejpam-3363	311	50	,	,	PUNCT
ejpam-3363	311	51	we	we	PRON
ejpam-3363	311	52	have	have	VERB
ejpam-3363	311	53	(	(	PUNCT
ejpam-3363	311	54	d	d	NOUN
ejpam-3363	311	55	)	)	PUNCT
ejpam-3363	311	56	∑	∑	PUNCT
ejpam-3363	311	57	e	e	X
ejpam-3363	311	58	[	[	PUNCT
ejpam-3363	311	59	‖fξ(wv	‖fξ(wv	ADJ
ejpam-3363	311	60	−wu)−	−wu)−	NOUN
ejpam-3363	311	61	f	f	X
ejpam-3363	311	62	(	(	PUNCT
ejpam-3363	311	63	u	u	NOUN
ejpam-3363	311	64	,	,	PUNCT
ejpam-3363	311	65	v)‖2v	v)‖2v	PROPN
ejpam-3363	311	66	]	]	PUNCT
ejpam-3363	312	1	<	<	X
ejpam-3363	312	2	ε	ε	PROPN
ejpam-3363	312	3	.	.	PROPN
ejpam-3363	312	4	4	4	NUM
ejpam-3363	312	5	.	.	X
ejpam-3363	312	6	descriptive	descriptive	ADJ
ejpam-3363	312	7	definition	definition	NOUN
ejpam-3363	312	8	of	of	ADP
ejpam-3363	312	9	itô-mcshane	itô-mcshane	VERB
ejpam-3363	312	10	integral	integral	ADJ
ejpam-3363	312	11	in	in	ADP
ejpam-3363	312	12	this	this	DET
ejpam-3363	312	13	section	section	NOUN
ejpam-3363	312	14	,	,	PUNCT
ejpam-3363	312	15	we	we	PRON
ejpam-3363	312	16	present	present	VERB
ejpam-3363	312	17	a	a	DET
ejpam-3363	312	18	version	version	NOUN
ejpam-3363	312	19	of	of	ADP
ejpam-3363	312	20	fundamental	fundamental	ADJ
ejpam-3363	312	21	theorem	theorem	NOUN
ejpam-3363	312	22	for	for	ADP
ejpam-3363	312	23	the	the	DET
ejpam-3363	312	24	itô-mcshane	itô-mcshane	NOUN
ejpam-3363	312	25	integral	integral	ADJ
ejpam-3363	312	26	of	of	ADP
ejpam-3363	312	27	an	an	DET
ejpam-3363	312	28	operator	operator	NOUN
ejpam-3363	312	29	-	-	PUNCT
ejpam-3363	312	30	valued	value	VERB
ejpam-3363	312	31	stochastic	stochastic	ADJ
ejpam-3363	312	32	process	process	NOUN
ejpam-3363	312	33	.	.	PUNCT
ejpam-3363	313	1	theorem	theorem	NOUN
ejpam-3363	313	2	3	3	X
ejpam-3363	313	3	.	.	PUNCT
ejpam-3363	314	1	let	let	VERB
ejpam-3363	314	2	f	f	PROPN
ejpam-3363	314	3	∈	∈	PROPN
ejpam-3363	314	4	λim	λim	X
ejpam-3363	314	5	and	and	CCONJ
ejpam-3363	314	6	let	let	VERB
ejpam-3363	314	7	f	f	PROPN
ejpam-3363	315	1	[	[	X
ejpam-3363	315	2	u	u	NOUN
ejpam-3363	315	3	,	,	PUNCT
ejpam-3363	315	4	v	v	NOUN
ejpam-3363	315	5	]	]	PUNCT
ejpam-3363	315	6	:	:	PUNCT
ejpam-3363	315	7	=	=	SYM
ejpam-3363	315	8	(	(	PUNCT
ejpam-3363	315	9	i	i	NOUN
ejpam-3363	315	10	m	m	VERB
ejpam-3363	315	11	)	)	PUNCT
ejpam-3363	315	12	∫	∫	PROPN
ejpam-3363	316	1	v	v	NUM
ejpam-3363	316	2	u	u	PROPN
ejpam-3363	316	3	f	f	PROPN
ejpam-3363	316	4	dw	dw	PROPN
ejpam-3363	316	5	for	for	ADP
ejpam-3363	316	6	all	all	DET
ejpam-3363	316	7	[	[	X
ejpam-3363	316	8	u	u	NOUN
ejpam-3363	316	9	,	,	PUNCT
ejpam-3363	316	10	v	v	ADP
ejpam-3363	316	11	]	]	X
ejpam-3363	316	12	⊂	⊂	PROPN
ejpam-3363	317	1	[	[	X
ejpam-3363	317	2	0	0	NUM
ejpam-3363	317	3	,	,	PUNCT
ejpam-3363	317	4	t	t	X
ejpam-3363	317	5	]	]	PUNCT
ejpam-3363	317	6	.	.	PUNCT
ejpam-3363	318	1	then	then	ADV
ejpam-3363	318	2	dft	dft	VERB
ejpam-3363	318	3	=	=	PUNCT
ejpam-3363	318	4	ft	ft	PROPN
ejpam-3363	318	5	a.e	a.e	PROPN
ejpam-3363	318	6	.	.	PROPN
ejpam-3363	319	1	on	on	ADP
ejpam-3363	319	2	[	[	X
ejpam-3363	319	3	0	0	NUM
ejpam-3363	319	4	,	,	PUNCT
ejpam-3363	319	5	t	t	NOUN
ejpam-3363	319	6	)	)	PUNCT
ejpam-3363	319	7	.	.	PUNCT
ejpam-3363	320	1	proof	proof	NOUN
ejpam-3363	320	2	.	.	PUNCT
ejpam-3363	321	1	let	let	VERB
ejpam-3363	321	2	a	a	PRON
ejpam-3363	321	3	=	=	SYM
ejpam-3363	321	4	{	{	PUNCT
ejpam-3363	321	5	t	t	NOUN
ejpam-3363	321	6	∈	∈	PROPN
ejpam-3363	322	1	[	[	X
ejpam-3363	322	2	0	0	NUM
ejpam-3363	322	3	,	,	PUNCT
ejpam-3363	322	4	t	t	PROPN
ejpam-3363	322	5	)	)	PUNCT
ejpam-3363	322	6	:	:	PUNCT
ejpam-3363	322	7	dft	dft	PROPN
ejpam-3363	322	8	does	do	AUX
ejpam-3363	322	9	not	not	PART
ejpam-3363	322	10	exist	exist	VERB
ejpam-3363	322	11	or	or	CCONJ
ejpam-3363	322	12	dft	dft	VERB
ejpam-3363	322	13	6=	6=	PROPN
ejpam-3363	322	14	ft	ft	PROPN
ejpam-3363	322	15	}	}	PUNCT
ejpam-3363	322	16	.	.	PUNCT
ejpam-3363	323	1	let	let	VERB
ejpam-3363	323	2	ξ	ξ	X
ejpam-3363	323	3	∈	∈	PROPN
ejpam-3363	323	4	a.	a.	NOUN
ejpam-3363	323	5	then	then	ADV
ejpam-3363	323	6	there	there	PRON
ejpam-3363	323	7	exists	exist	VERB
ejpam-3363	323	8	γ(ξ	γ(ξ	PROPN
ejpam-3363	323	9	)	)	PUNCT
ejpam-3363	323	10	>	>	X
ejpam-3363	323	11	0	0	PUNCT
ejpam-3363	323	12	such	such	ADJ
ejpam-3363	323	13	that	that	PRON
ejpam-3363	323	14	for	for	ADP
ejpam-3363	323	15	every	every	DET
ejpam-3363	323	16	positive	positive	ADJ
ejpam-3363	323	17	function	function	NOUN
ejpam-3363	323	18	δ	δ	PROPN
ejpam-3363	323	19	on	on	ADP
ejpam-3363	323	20	[	[	X
ejpam-3363	323	21	0	0	NUM
ejpam-3363	323	22	,	,	PUNCT
ejpam-3363	323	23	t	t	X
ejpam-3363	323	24	]	]	PUNCT
ejpam-3363	323	25	,	,	PUNCT
ejpam-3363	323	26	there	there	PRON
ejpam-3363	323	27	exists	exist	VERB
ejpam-3363	323	28	a	a	PRON
ejpam-3363	323	29	δ	δ	NOUN
ejpam-3363	323	30	-	-	PUNCT
ejpam-3363	323	31	fine	fine	NOUN
ejpam-3363	323	32	belated	belate	VERB
ejpam-3363	323	33	mcshane	mcshane	PROPN
ejpam-3363	323	34	interval	interval	NOUN
ejpam-3363	323	35	-	-	PUNCT
ejpam-3363	323	36	point	point	NOUN
ejpam-3363	323	37	pair	pair	NOUN
ejpam-3363	323	38	(	(	PUNCT
ejpam-3363	324	1	[	[	X
ejpam-3363	324	2	u	u	NOUN
ejpam-3363	324	3	,	,	PUNCT
ejpam-3363	324	4	v	v	ADP
ejpam-3363	324	5	]	]	X
ejpam-3363	324	6	,	,	PUNCT
ejpam-3363	324	7	ξ	ξ	X
ejpam-3363	324	8	)	)	PUNCT
ejpam-3363	324	9	of	of	ADP
ejpam-3363	324	10	[	[	X
ejpam-3363	324	11	0	0	NUM
ejpam-3363	324	12	,	,	PUNCT
ejpam-3363	324	13	t	t	X
ejpam-3363	324	14	]	]	PUNCT
ejpam-3363	324	15	with	with	ADP
ejpam-3363	324	16	e	e	X
ejpam-3363	324	17	[	[	PUNCT
ejpam-3363	324	18	‖fξ(wv	‖fξ(wv	PROPN
ejpam-3363	324	19	−wu)−	−wu)−	NOUN
ejpam-3363	324	20	f	f	NOUN
ejpam-3363	325	1	[	[	X
ejpam-3363	325	2	u	u	NOUN
ejpam-3363	325	3	,	,	PUNCT
ejpam-3363	325	4	v]‖2v	v]‖2v	PROPN
ejpam-3363	325	5	]	]	PUNCT
ejpam-3363	325	6	≥	≥	NOUN
ejpam-3363	325	7	γ(ξ)(v	γ(ξ)(v	X
ejpam-3363	325	8	−	−	PROPN
ejpam-3363	325	9	u	u	NOUN
ejpam-3363	325	10	)	)	PUNCT
ejpam-3363	325	11	.	.	PUNCT
ejpam-3363	326	1	(	(	PUNCT
ejpam-3363	326	2	9	9	X
ejpam-3363	326	3	)	)	PUNCT
ejpam-3363	326	4	j.d	j.d	PROPN
ejpam-3363	326	5	.	.	PROPN
ejpam-3363	326	6	cagubcob	cagubcob	PROPN
ejpam-3363	326	7	,	,	PUNCT
ejpam-3363	326	8	m.	m.	NOUN
ejpam-3363	326	9	labendia	labendia	PROPN
ejpam-3363	326	10	/	/	SYM
ejpam-3363	326	11	eur	eur	PROPN
ejpam-3363	326	12	.	.	PUNCT
ejpam-3363	327	1	j.	j.	PROPN
ejpam-3363	327	2	pure	pure	PROPN
ejpam-3363	327	3	appl	appl	PROPN
ejpam-3363	327	4	.	.	PROPN
ejpam-3363	327	5	math	math	PROPN
ejpam-3363	327	6	,	,	PUNCT
ejpam-3363	327	7	12	12	NUM
ejpam-3363	327	8	(	(	PUNCT
ejpam-3363	327	9	1	1	NUM
ejpam-3363	327	10	)	)	PUNCT
ejpam-3363	327	11	(	(	PUNCT
ejpam-3363	327	12	2019	2019	NUM
ejpam-3363	327	13	)	)	PUNCT
ejpam-3363	327	14	,	,	PUNCT
ejpam-3363	327	15	101	101	NUM
ejpam-3363	327	16	-	-	SYM
ejpam-3363	327	17	117	117	NUM
ejpam-3363	327	18	113	113	NUM
ejpam-3363	327	19	let	let	VERB
ejpam-3363	327	20	ε	ε	PROPN
ejpam-3363	327	21	>	>	X
ejpam-3363	327	22	0	0	PROPN
ejpam-3363	327	23	.	.	PUNCT
ejpam-3363	328	1	by	by	ADP
ejpam-3363	328	2	the	the	DET
ejpam-3363	328	3	strong	strong	ADJ
ejpam-3363	328	4	version	version	NOUN
ejpam-3363	328	5	of	of	ADP
ejpam-3363	328	6	saks	sak	NOUN
ejpam-3363	328	7	-	-	PUNCT
ejpam-3363	328	8	henstock	henstock	NOUN
ejpam-3363	328	9	lemma	lemma	PROPN
ejpam-3363	328	10	(	(	PUNCT
ejpam-3363	328	11	lemma	lemma	PROPN
ejpam-3363	328	12	7	7	NUM
ejpam-3363	328	13	)	)	PUNCT
ejpam-3363	328	14	,	,	PUNCT
ejpam-3363	328	15	there	there	PRON
ejpam-3363	328	16	exists	exist	VERB
ejpam-3363	328	17	a	a	DET
ejpam-3363	328	18	positive	positive	ADJ
ejpam-3363	328	19	function	function	NOUN
ejpam-3363	328	20	δ1	δ1	NOUN
ejpam-3363	328	21	on	on	ADP
ejpam-3363	328	22	[	[	X
ejpam-3363	328	23	0	0	NUM
ejpam-3363	328	24	,	,	PUNCT
ejpam-3363	328	25	t	t	X
ejpam-3363	328	26	]	]	PUNCT
ejpam-3363	328	27	such	such	ADJ
ejpam-3363	328	28	that	that	SCONJ
ejpam-3363	328	29	for	for	ADP
ejpam-3363	328	30	any	any	DET
ejpam-3363	328	31	δ1	δ1	NOUN
ejpam-3363	328	32	-	-	PUNCT
ejpam-3363	328	33	fine	fine	NOUN
ejpam-3363	328	34	belated	belate	VERB
ejpam-3363	328	35	mcshane	mcshane	PROPN
ejpam-3363	328	36	partial	partial	ADJ
ejpam-3363	328	37	division	division	NOUN
ejpam-3363	328	38	d	d	NOUN
ejpam-3363	328	39	=	=	PRON
ejpam-3363	328	40	{	{	PUNCT
ejpam-3363	328	41	(	(	PUNCT
ejpam-3363	328	42	[	[	X
ejpam-3363	328	43	u	u	NOUN
ejpam-3363	328	44	,	,	PUNCT
ejpam-3363	328	45	v	v	ADP
ejpam-3363	328	46	]	]	X
ejpam-3363	328	47	,	,	PUNCT
ejpam-3363	328	48	ξ	ξ	X
ejpam-3363	328	49	)	)	PUNCT
ejpam-3363	328	50	}	}	PUNCT
ejpam-3363	328	51	of	of	ADP
ejpam-3363	328	52	[	[	X
ejpam-3363	328	53	0	0	NUM
ejpam-3363	328	54	,	,	PUNCT
ejpam-3363	328	55	t	t	X
ejpam-3363	328	56	]	]	PUNCT
ejpam-3363	328	57	,	,	PUNCT
ejpam-3363	328	58	we	we	PRON
ejpam-3363	328	59	have	have	VERB
ejpam-3363	328	60	(	(	PUNCT
ejpam-3363	328	61	d	d	NOUN
ejpam-3363	328	62	)	)	PUNCT
ejpam-3363	328	63	∑	∑	PUNCT
ejpam-3363	328	64	e	e	X
ejpam-3363	328	65	[	[	PUNCT
ejpam-3363	328	66	‖fξ(wv	‖fξ(wv	ADJ
ejpam-3363	328	67	−wu)−	−wu)−	NOUN
ejpam-3363	328	68	f	f	NOUN
ejpam-3363	329	1	[	[	X
ejpam-3363	329	2	u	u	NOUN
ejpam-3363	329	3	,	,	PUNCT
ejpam-3363	329	4	v]‖2v	v]‖2v	X
ejpam-3363	329	5	]	]	PUNCT
ejpam-3363	329	6	<	<	X
ejpam-3363	329	7	ε	ε	PROPN
ejpam-3363	329	8	.	.	PUNCT
ejpam-3363	330	1	(	(	PUNCT
ejpam-3363	330	2	10	10	NUM
ejpam-3363	330	3	)	)	PUNCT
ejpam-3363	330	4	let	let	VERB
ejpam-3363	330	5	ξ1	ξ1	NOUN
ejpam-3363	330	6	,	,	PUNCT
ejpam-3363	330	7	ξ2	ξ2	ADJ
ejpam-3363	330	8	,	,	PUNCT
ejpam-3363	330	9	.	.	PUNCT
ejpam-3363	330	10	.	.	PUNCT
ejpam-3363	331	1	.	.	PUNCT
ejpam-3363	332	1	,	,	PUNCT
ejpam-3363	332	2	ξn	ξn	PROPN
ejpam-3363	332	3	∈	∈	PROPN
ejpam-3363	332	4	a.	a.	NOUN
ejpam-3363	332	5	by	by	ADP
ejpam-3363	332	6	(	(	PUNCT
ejpam-3363	332	7	9	9	NUM
ejpam-3363	332	8	)	)	PUNCT
ejpam-3363	332	9	,	,	PUNCT
ejpam-3363	332	10	each	each	DET
ejpam-3363	332	11	ξi	ξi	NOUN
ejpam-3363	332	12	corresponds	correspond	VERB
ejpam-3363	332	13	a	a	DET
ejpam-3363	332	14	δ1	δ1	NOUN
ejpam-3363	332	15	-	-	PUNCT
ejpam-3363	332	16	fine	fine	NOUN
ejpam-3363	332	17	belated	belate	VERB
ejpam-3363	332	18	interval	interval	NOUN
ejpam-3363	332	19	[	[	X
ejpam-3363	332	20	ui	ui	PROPN
ejpam-3363	332	21	,	,	PUNCT
ejpam-3363	332	22	vi	vi	PROPN
ejpam-3363	332	23	]	]	PUNCT
ejpam-3363	332	24	,	,	PUNCT
ejpam-3363	332	25	for	for	ADP
ejpam-3363	332	26	i	i	PROPN
ejpam-3363	332	27	=	=	SYM
ejpam-3363	332	28	1	1	NUM
ejpam-3363	332	29	,	,	PUNCT
ejpam-3363	332	30	2	2	NUM
ejpam-3363	332	31	,	,	PUNCT
ejpam-3363	332	32	.	.	PUNCT
ejpam-3363	332	33	.	.	PUNCT
ejpam-3363	333	1	.	.	PUNCT
ejpam-3363	334	1	,	,	PUNCT
ejpam-3363	334	2	n.	n.	PROPN
ejpam-3363	334	3	thus	thus	ADV
ejpam-3363	334	4	,	,	PUNCT
ejpam-3363	334	5	n∑	n∑	PROPN
ejpam-3363	334	6	i=1	i=1	X
ejpam-3363	334	7	γ(ξi)(vi	γ(ξi)(vi	X
ejpam-3363	334	8	−	−	PROPN
ejpam-3363	334	9	ui	ui	NOUN
ejpam-3363	334	10	)	)	PUNCT
ejpam-3363	334	11	≤	≤	PUNCT
ejpam-3363	335	1	n∑	n∑	X
ejpam-3363	335	2	i=1	i=1	PROPN
ejpam-3363	336	1	e	e	X
ejpam-3363	336	2	[	[	PUNCT
ejpam-3363	336	3	‖fξi(wvi	‖fξi(wvi	X
ejpam-3363	336	4	−wui)−	−wui)−	NOUN
ejpam-3363	336	5	f	f	PROPN
ejpam-3363	337	1	[	[	X
ejpam-3363	337	2	ui	ui	PROPN
ejpam-3363	337	3	,	,	PUNCT
ejpam-3363	337	4	vi]‖2v	vi]‖2v	X
ejpam-3363	337	5	]	]	PUNCT
ejpam-3363	337	6	<	<	X
ejpam-3363	337	7	ε	ε	PROPN
ejpam-3363	337	8	.	.	PROPN
ejpam-3363	337	9	for	for	ADP
ejpam-3363	337	10	m	m	PROPN
ejpam-3363	337	11	∈	∈	PROPN
ejpam-3363	337	12	n	n	CCONJ
ejpam-3363	337	13	,	,	PUNCT
ejpam-3363	337	14	let	let	VERB
ejpam-3363	337	15	am	be	AUX
ejpam-3363	337	16	=	=	PRON
ejpam-3363	337	17	{	{	PUNCT
ejpam-3363	337	18	t	t	PROPN
ejpam-3363	337	19	∈	∈	PROPN
ejpam-3363	337	20	a	a	DET
ejpam-3363	337	21	:	:	PUNCT
ejpam-3363	337	22	γ(t	γ(t	NOUN
ejpam-3363	337	23	)	)	PUNCT
ejpam-3363	337	24	≥	≥	NOUN
ejpam-3363	337	25	1	1	NUM
ejpam-3363	337	26	m	m	NOUN
ejpam-3363	337	27	}	}	PUNCT
ejpam-3363	337	28	.	.	PUNCT
ejpam-3363	338	1	then	then	ADV
ejpam-3363	338	2	a	a	DET
ejpam-3363	338	3	=	=	PUNCT
ejpam-3363	338	4	⋃	⋃	PROPN
ejpam-3363	338	5	m∈n	m∈n	NOUN
ejpam-3363	338	6	am	be	AUX
ejpam-3363	338	7	.	.	PUNCT
ejpam-3363	339	1	hence	hence	ADV
ejpam-3363	339	2	,	,	PUNCT
ejpam-3363	339	3	for	for	ADP
ejpam-3363	339	4	all	all	PRON
ejpam-3363	339	5	i	i	PRON
ejpam-3363	339	6	∈	∈	PROPN
ejpam-3363	339	7	{	{	PUNCT
ejpam-3363	339	8	1	1	NUM
ejpam-3363	339	9	,	,	PUNCT
ejpam-3363	339	10	2	2	NUM
ejpam-3363	339	11	,	,	PUNCT
ejpam-3363	339	12	.	.	PUNCT
ejpam-3363	339	13	.	.	PUNCT
ejpam-3363	339	14	.	.	PUNCT
ejpam-3363	339	15	,	,	PUNCT
ejpam-3363	339	16	n	n	CCONJ
ejpam-3363	339	17	}	}	PUNCT
ejpam-3363	339	18	,	,	PUNCT
ejpam-3363	339	19	ξi	ξi	NUM
ejpam-3363	339	20	∈	∈	NOUN
ejpam-3363	339	21	ami	ami	NOUN
ejpam-3363	339	22	for	for	ADP
ejpam-3363	339	23	some	some	DET
ejpam-3363	339	24	mi	mi	PROPN
ejpam-3363	339	25	∈	∈	PROPN
ejpam-3363	339	26	n.	n.	NOUN
ejpam-3363	339	27	let	let	VERB
ejpam-3363	339	28	m	m	PRON
ejpam-3363	339	29	:	:	PUNCT
ejpam-3363	339	30	max{mi	max{mi	NOUN
ejpam-3363	339	31	:	:	PUNCT
ejpam-3363	340	1	i	i	PRON
ejpam-3363	340	2	=	=	NOUN
ejpam-3363	340	3	1	1	NUM
ejpam-3363	340	4	,	,	PUNCT
ejpam-3363	340	5	2	2	NUM
ejpam-3363	340	6	,	,	PUNCT
ejpam-3363	340	7	.	.	PUNCT
ejpam-3363	340	8	.	.	PUNCT
ejpam-3363	340	9	.	.	PUNCT
ejpam-3363	340	10	,	,	PUNCT
ejpam-3363	340	11	n	n	CCONJ
ejpam-3363	340	12	}	}	PUNCT
ejpam-3363	340	13	.	.	PUNCT
ejpam-3363	341	1	then	then	ADV
ejpam-3363	341	2	n∑	n∑	PROPN
ejpam-3363	341	3	i=1	i=1	PROPN
ejpam-3363	341	4	1	1	NUM
ejpam-3363	341	5	m	m	PROPN
ejpam-3363	341	6	(	(	PUNCT
ejpam-3363	341	7	vi	vi	NOUN
ejpam-3363	341	8	−	−	PROPN
ejpam-3363	341	9	ui	ui	NOUN
ejpam-3363	341	10	)	)	PUNCT
ejpam-3363	341	11	≤	≤	PUNCT
ejpam-3363	342	1	n∑	n∑	NOUN
ejpam-3363	342	2	i=1	i=1	ADP
ejpam-3363	343	1	γ(ξi)(vi	γ(ξi)(vi	X
ejpam-3363	343	2	−	−	PROPN
ejpam-3363	343	3	ui	ui	NOUN
ejpam-3363	343	4	)	)	PUNCT
ejpam-3363	343	5	<	<	X
ejpam-3363	343	6	ε	ε	PROPN
ejpam-3363	343	7	which	which	PRON
ejpam-3363	343	8	implies	imply	VERB
ejpam-3363	343	9	that	that	SCONJ
ejpam-3363	343	10	n∑	n∑	PROPN
ejpam-3363	343	11	i=1	i=1	PROPN
ejpam-3363	343	12	(	(	PUNCT
ejpam-3363	343	13	vi−ui	vi−ui	NOUN
ejpam-3363	343	14	)	)	PUNCT
ejpam-3363	343	15	<	<	X
ejpam-3363	344	1	mε	mε	X
ejpam-3363	344	2	.	.	PUNCT
ejpam-3363	345	1	let	let	VERB
ejpam-3363	345	2	v	v	PART
ejpam-3363	345	3	be	be	AUX
ejpam-3363	345	4	the	the	DET
ejpam-3363	345	5	family	family	NOUN
ejpam-3363	345	6	of	of	ADP
ejpam-3363	345	7	interval	interval	NOUN
ejpam-3363	345	8	-	-	PUNCT
ejpam-3363	345	9	point	point	NOUN
ejpam-3363	345	10	pairs	pair	NOUN
ejpam-3363	345	11	{	{	PUNCT
ejpam-3363	345	12	(	(	PUNCT
ejpam-3363	345	13	[	[	X
ejpam-3363	345	14	u	u	NOUN
ejpam-3363	345	15	,	,	PUNCT
ejpam-3363	345	16	v	v	ADP
ejpam-3363	345	17	]	]	X
ejpam-3363	345	18	,	,	PUNCT
ejpam-3363	345	19	ξ	ξ	X
ejpam-3363	345	20	)	)	PUNCT
ejpam-3363	345	21	}	}	PUNCT
ejpam-3363	345	22	induced	induce	VERB
ejpam-3363	345	23	from	from	ADP
ejpam-3363	345	24	all	all	DET
ejpam-3363	345	25	δ1	δ1	NOUN
ejpam-3363	345	26	-	-	PUNCT
ejpam-3363	345	27	fine	fine	NOUN
ejpam-3363	345	28	belated	belate	VERB
ejpam-3363	345	29	mcshane	mcshane	PROPN
ejpam-3363	345	30	partial	partial	ADJ
ejpam-3363	345	31	division	division	NOUN
ejpam-3363	345	32	of	of	ADP
ejpam-3363	345	33	[	[	X
ejpam-3363	345	34	0	0	NUM
ejpam-3363	345	35	,	,	PUNCT
ejpam-3363	345	36	t	t	X
ejpam-3363	345	37	]	]	PUNCT
ejpam-3363	345	38	such	such	ADJ
ejpam-3363	345	39	that	that	SCONJ
ejpam-3363	345	40	ξ	ξ	PROPN
ejpam-3363	345	41	∈	∈	PROPN
ejpam-3363	345	42	am	be	AUX
ejpam-3363	345	43	.	.	PUNCT
ejpam-3363	346	1	then	then	ADV
ejpam-3363	346	2	v	v	NOUN
ejpam-3363	346	3	is	be	AUX
ejpam-3363	346	4	a	a	DET
ejpam-3363	346	5	vitali	vitali	ADJ
ejpam-3363	346	6	cover	cover	NOUN
ejpam-3363	346	7	of	of	ADP
ejpam-3363	346	8	am	be	AUX
ejpam-3363	346	9	.	.	PUNCT
ejpam-3363	347	1	applying	apply	VERB
ejpam-3363	347	2	the	the	DET
ejpam-3363	347	3	vitali	vitali	PROPN
ejpam-3363	347	4	covering	cover	VERB
ejpam-3363	347	5	lemma	lemma	PROPN
ejpam-3363	347	6	,	,	PUNCT
ejpam-3363	347	7	there	there	PRON
ejpam-3363	347	8	exists	exist	VERB
ejpam-3363	347	9	a	a	DET
ejpam-3363	347	10	finite	finite	ADJ
ejpam-3363	347	11	collection	collection	NOUN
ejpam-3363	347	12	{	{	PUNCT
ejpam-3363	347	13	(	(	PUNCT
ejpam-3363	347	14	[	[	X
ejpam-3363	347	15	ui	ui	NOUN
ejpam-3363	347	16	,	,	PUNCT
ejpam-3363	347	17	vi	vi	PROPN
ejpam-3363	347	18	]	]	PUNCT
ejpam-3363	347	19	,	,	PUNCT
ejpam-3363	347	20	ξi)}ni=1	ξi)}ni=1	PROPN
ejpam-3363	347	21	in	in	ADP
ejpam-3363	347	22	v	v	ADP
ejpam-3363	347	23	such	such	ADJ
ejpam-3363	347	24	that	that	DET
ejpam-3363	347	25	leb∗(am	leb∗(am	NOUN
ejpam-3363	347	26	)	)	PUNCT
ejpam-3363	348	1	<	<	X
ejpam-3363	348	2	n∑	n∑	PROPN
ejpam-3363	348	3	i=1	i=1	PROPN
ejpam-3363	349	1	(	(	PUNCT
ejpam-3363	349	2	vi	vi	NOUN
ejpam-3363	349	3	−	−	PROPN
ejpam-3363	349	4	ui	ui	NOUN
ejpam-3363	349	5	)	)	PUNCT
ejpam-3363	350	1	+	+	CCONJ
ejpam-3363	350	2	ε	ε	X
ejpam-3363	350	3	<	<	X
ejpam-3363	350	4	(	(	PUNCT
ejpam-3363	350	5	m+	m+	NOUN
ejpam-3363	350	6	1)ε	1)ε	NUM
ejpam-3363	350	7	.	.	PUNCT
ejpam-3363	351	1	since	since	SCONJ
ejpam-3363	351	2	ε	ε	PROPN
ejpam-3363	351	3	is	be	AUX
ejpam-3363	351	4	arbitrary	arbitrary	ADJ
ejpam-3363	351	5	,	,	PUNCT
ejpam-3363	351	6	leb(am	leb(am	NUM
ejpam-3363	351	7	)	)	PUNCT
ejpam-3363	352	1	=	=	SYM
ejpam-3363	352	2	0	0	X
ejpam-3363	352	3	.	.	PUNCT
ejpam-3363	353	1	thus	thus	ADV
ejpam-3363	353	2	,	,	PUNCT
ejpam-3363	353	3	leb(a	leb(a	PROPN
ejpam-3363	353	4	)	)	PUNCT
ejpam-3363	353	5	=	=	SYM
ejpam-3363	353	6	0	0	X
ejpam-3363	353	7	.	.	PUNCT
ejpam-3363	353	8	theorem	theorem	NOUN
ejpam-3363	353	9	4	4	NUM
ejpam-3363	353	10	.	.	PUNCT
ejpam-3363	354	1	let	let	VERB
ejpam-3363	354	2	f	f	NOUN
ejpam-3363	354	3	:	:	PUNCT
ejpam-3363	355	1	[	[	X
ejpam-3363	355	2	0	0	NUM
ejpam-3363	355	3	,	,	PUNCT
ejpam-3363	355	4	t	t	X
ejpam-3363	355	5	]	]	X
ejpam-3363	355	6	×	×	PROPN
ejpam-3363	355	7	ω→	ω→	SYM
ejpam-3363	355	8	l(u	l(u	PROPN
ejpam-3363	355	9	,	,	PUNCT
ejpam-3363	355	10	v	v	NOUN
ejpam-3363	355	11	)	)	PUNCT
ejpam-3363	355	12	be	be	AUX
ejpam-3363	355	13	an	an	DET
ejpam-3363	355	14	adapted	adapt	VERB
ejpam-3363	355	15	process	process	NOUN
ejpam-3363	355	16	and	and	CCONJ
ejpam-3363	355	17	let	let	VERB
ejpam-3363	355	18	f	f	PRON
ejpam-3363	355	19	:	:	PUNCT
ejpam-3363	355	20	j	j	PROPN
ejpam-3363	355	21	×	×	PROPN
ejpam-3363	355	22	ω→	ω→	NUM
ejpam-3363	355	23	v	v	NOUN
ejpam-3363	355	24	be	be	AUX
ejpam-3363	355	25	ac2[0	ac2[0	ADJ
ejpam-3363	355	26	,	,	PUNCT
ejpam-3363	355	27	t	t	X
ejpam-3363	355	28	]	]	PUNCT
ejpam-3363	355	29	,	,	PUNCT
ejpam-3363	355	30	has	have	VERB
ejpam-3363	355	31	the	the	DET
ejpam-3363	355	32	orthogonal	orthogonal	ADJ
ejpam-3363	355	33	increment	increment	NOUN
ejpam-3363	355	34	property	property	NOUN
ejpam-3363	355	35	,	,	PUNCT
ejpam-3363	355	36	and	and	CCONJ
ejpam-3363	355	37	dft	dft	PROPN
ejpam-3363	355	38	=	=	SYM
ejpam-3363	355	39	ft	ft	PROPN
ejpam-3363	355	40	a.e	a.e	PROPN
ejpam-3363	355	41	.	.	PROPN
ejpam-3363	356	1	on	on	ADP
ejpam-3363	356	2	[	[	X
ejpam-3363	356	3	0	0	NUM
ejpam-3363	356	4	,	,	PUNCT
ejpam-3363	356	5	t	t	NOUN
ejpam-3363	356	6	)	)	PUNCT
ejpam-3363	356	7	.	.	PUNCT
ejpam-3363	357	1	then	then	ADV
ejpam-3363	357	2	f	f	PROPN
ejpam-3363	357	3	∈	∈	PROPN
ejpam-3363	357	4	λim	λim	X
ejpam-3363	357	5	and	and	CCONJ
ejpam-3363	357	6	f	f	X
ejpam-3363	358	1	[	[	X
ejpam-3363	358	2	u	u	NOUN
ejpam-3363	358	3	,	,	PUNCT
ejpam-3363	358	4	v	v	NOUN
ejpam-3363	358	5	]	]	PUNCT
ejpam-3363	358	6	:	:	PUNCT
ejpam-3363	358	7	=	=	SYM
ejpam-3363	358	8	(	(	PUNCT
ejpam-3363	358	9	i	i	NOUN
ejpam-3363	358	10	m	m	VERB
ejpam-3363	358	11	)	)	PUNCT
ejpam-3363	358	12	∫	∫	PROPN
ejpam-3363	359	1	v	v	NUM
ejpam-3363	359	2	u	u	PROPN
ejpam-3363	359	3	fs	fs	ADP
ejpam-3363	359	4	dws	dws	PROPN
ejpam-3363	359	5	for	for	ADP
ejpam-3363	359	6	all	all	DET
ejpam-3363	359	7	[	[	X
ejpam-3363	359	8	u	u	NOUN
ejpam-3363	359	9	,	,	PUNCT
ejpam-3363	359	10	v	v	ADP
ejpam-3363	359	11	]	]	X
ejpam-3363	359	12	⊂	⊂	PROPN
ejpam-3363	360	1	[	[	X
ejpam-3363	360	2	0	0	NUM
ejpam-3363	360	3	,	,	PUNCT
ejpam-3363	360	4	t	t	X
ejpam-3363	360	5	]	]	PUNCT
ejpam-3363	360	6	.	.	PUNCT
ejpam-3363	361	1	proof	proof	NOUN
ejpam-3363	361	2	.	.	PUNCT
ejpam-3363	362	1	let	let	VERB
ejpam-3363	362	2	a	a	PRON
ejpam-3363	362	3	=	=	SYM
ejpam-3363	362	4	{	{	PUNCT
ejpam-3363	362	5	t	t	NOUN
ejpam-3363	362	6	∈	∈	PROPN
ejpam-3363	363	1	[	[	X
ejpam-3363	363	2	0	0	NUM
ejpam-3363	363	3	,	,	PUNCT
ejpam-3363	363	4	t	t	PROPN
ejpam-3363	363	5	)	)	PUNCT
ejpam-3363	363	6	:	:	PUNCT
ejpam-3363	363	7	dft	dft	PROPN
ejpam-3363	363	8	does	do	AUX
ejpam-3363	363	9	not	not	PART
ejpam-3363	363	10	exist	exist	VERB
ejpam-3363	363	11	or	or	CCONJ
ejpam-3363	363	12	dft	dft	VERB
ejpam-3363	363	13	6=	6=	PROPN
ejpam-3363	363	14	ft	ft	PROPN
ejpam-3363	363	15	}	}	PUNCT
ejpam-3363	363	16	.	.	PUNCT
ejpam-3363	364	1	then	then	ADV
ejpam-3363	364	2	leb(a	leb(a	NUM
ejpam-3363	364	3	)	)	PUNCT
ejpam-3363	364	4	=	=	SYM
ejpam-3363	364	5	0	0	X
ejpam-3363	364	6	.	.	PUNCT
ejpam-3363	365	1	let	let	VERB
ejpam-3363	365	2	ξ	ξ	X
ejpam-3363	365	3	∈	∈	NOUN
ejpam-3363	365	4	ac	ac	PROPN
ejpam-3363	366	1	:	:	PUNCT
ejpam-3363	366	2	=	=	SYM
ejpam-3363	367	1	[	[	X
ejpam-3363	367	2	0	0	NUM
ejpam-3363	367	3	,	,	PUNCT
ejpam-3363	367	4	t	t	X
ejpam-3363	367	5	]	]	PUNCT
ejpam-3363	367	6	\a	\a	NUM
ejpam-3363	367	7	.	.	PUNCT
ejpam-3363	368	1	then	then	ADV
ejpam-3363	368	2	for	for	ADP
ejpam-3363	368	3	every	every	DET
ejpam-3363	368	4	ε	ε	PROPN
ejpam-3363	368	5	>	>	X
ejpam-3363	368	6	0	0	PROPN
ejpam-3363	368	7	,	,	PUNCT
ejpam-3363	368	8	there	there	PRON
ejpam-3363	368	9	exists	exist	VERB
ejpam-3363	368	10	a	a	DET
ejpam-3363	368	11	positive	positive	ADJ
ejpam-3363	368	12	function	function	NOUN
ejpam-3363	368	13	δ1	δ1	NOUN
ejpam-3363	368	14	on	on	ADP
ejpam-3363	368	15	[	[	X
ejpam-3363	368	16	0	0	NUM
ejpam-3363	368	17	,	,	PUNCT
ejpam-3363	368	18	t	t	X
ejpam-3363	368	19	]	]	PUNCT
ejpam-3363	368	20	such	such	ADJ
ejpam-3363	368	21	that	that	SCONJ
ejpam-3363	368	22	for	for	ADP
ejpam-3363	368	23	any	any	DET
ejpam-3363	368	24	δ1	δ1	NOUN
ejpam-3363	368	25	-	-	PUNCT
ejpam-3363	368	26	fine	fine	NOUN
ejpam-3363	368	27	belated	belate	VERB
ejpam-3363	368	28	mcshane	mcshane	PROPN
ejpam-3363	368	29	interval	interval	NOUN
ejpam-3363	368	30	-	-	PUNCT
ejpam-3363	368	31	point	point	NOUN
ejpam-3363	368	32	pair	pair	NOUN
ejpam-3363	368	33	(	(	PUNCT
ejpam-3363	368	34	[	[	X
ejpam-3363	368	35	u	u	NOUN
ejpam-3363	368	36	,	,	PUNCT
ejpam-3363	368	37	v	v	ADP
ejpam-3363	368	38	]	]	X
ejpam-3363	368	39	,	,	PUNCT
ejpam-3363	368	40	ξ	ξ	X
ejpam-3363	368	41	)	)	PUNCT
ejpam-3363	368	42	of	of	ADP
ejpam-3363	368	43	[	[	X
ejpam-3363	368	44	0	0	NUM
ejpam-3363	368	45	,	,	PUNCT
ejpam-3363	368	46	t	t	X
ejpam-3363	368	47	]	]	PUNCT
ejpam-3363	368	48	,	,	PUNCT
ejpam-3363	368	49	we	we	PRON
ejpam-3363	368	50	have	have	VERB
ejpam-3363	368	51	e	e	X
ejpam-3363	368	52	[	[	PUNCT
ejpam-3363	368	53	‖fξ(wv	‖fξ(wv	VERB
ejpam-3363	368	54	−wu)−	−wu)−	NOUN
ejpam-3363	368	55	f	f	NOUN
ejpam-3363	369	1	[	[	X
ejpam-3363	369	2	u	u	NOUN
ejpam-3363	369	3	,	,	PUNCT
ejpam-3363	369	4	v]‖2v	v]‖2v	X
ejpam-3363	369	5	]	]	PUNCT
ejpam-3363	369	6	<	<	X
ejpam-3363	369	7	ε	ε	PROPN
ejpam-3363	369	8	4	4	NUM
ejpam-3363	369	9	t	t	PROPN
ejpam-3363	369	10	(	(	PUNCT
ejpam-3363	369	11	v	v	NOUN
ejpam-3363	369	12	−	−	PROPN
ejpam-3363	369	13	u	u	NOUN
ejpam-3363	369	14	)	)	PUNCT
ejpam-3363	369	15	.	.	PUNCT
ejpam-3363	370	1	let	let	VERB
ejpam-3363	370	2	d1	d1	PROPN
ejpam-3363	370	3	=	=	PUNCT
ejpam-3363	370	4	{	{	PUNCT
ejpam-3363	370	5	(	(	PUNCT
ejpam-3363	370	6	[	[	X
ejpam-3363	370	7	ui	ui	NOUN
ejpam-3363	370	8	,	,	PUNCT
ejpam-3363	370	9	vi	vi	PROPN
ejpam-3363	370	10	]	]	PUNCT
ejpam-3363	370	11	,	,	PUNCT
ejpam-3363	370	12	ξi)}ni=1	ξi)}ni=1	PROPN
ejpam-3363	370	13	be	be	VERB
ejpam-3363	370	14	a	a	DET
ejpam-3363	370	15	δ1	δ1	NOUN
ejpam-3363	370	16	-	-	PUNCT
ejpam-3363	370	17	fine	fine	NOUN
ejpam-3363	370	18	belated	belate	VERB
ejpam-3363	370	19	mcshane	mcshane	PROPN
ejpam-3363	370	20	partial	partial	ADJ
ejpam-3363	370	21	division	division	NOUN
ejpam-3363	370	22	on	on	ADP
ejpam-3363	370	23	[	[	X
ejpam-3363	370	24	0	0	NUM
ejpam-3363	370	25	,	,	PUNCT
ejpam-3363	370	26	t	t	X
ejpam-3363	370	27	]	]	PUNCT
ejpam-3363	370	28	with	with	ADP
ejpam-3363	370	29	ξi	ξi	PROPN
ejpam-3363	370	30	∈	∈	PROPN
ejpam-3363	370	31	ac	ac	PROPN
ejpam-3363	370	32	.	.	PUNCT
ejpam-3363	371	1	then	then	ADV
ejpam-3363	371	2	by	by	ADP
ejpam-3363	371	3	lemma	lemma	PROPN
ejpam-3363	371	4	3	3	NUM
ejpam-3363	371	5	,	,	PUNCT
ejpam-3363	371	6	j.d	j.d	PROPN
ejpam-3363	371	7	.	.	PROPN
ejpam-3363	371	8	cagubcob	cagubcob	PROPN
ejpam-3363	371	9	,	,	PUNCT
ejpam-3363	371	10	m.	m.	NOUN
ejpam-3363	371	11	labendia	labendia	PROPN
ejpam-3363	371	12	/	/	SYM
ejpam-3363	371	13	eur	eur	PROPN
ejpam-3363	371	14	.	.	PUNCT
ejpam-3363	372	1	j.	j.	PROPN
ejpam-3363	372	2	pure	pure	PROPN
ejpam-3363	372	3	appl	appl	PROPN
ejpam-3363	372	4	.	.	PROPN
ejpam-3363	372	5	math	math	PROPN
ejpam-3363	372	6	,	,	PUNCT
ejpam-3363	372	7	12	12	NUM
ejpam-3363	372	8	(	(	PUNCT
ejpam-3363	372	9	1	1	NUM
ejpam-3363	372	10	)	)	PUNCT
ejpam-3363	372	11	(	(	PUNCT
ejpam-3363	372	12	2019	2019	NUM
ejpam-3363	372	13	)	)	PUNCT
ejpam-3363	372	14	,	,	PUNCT
ejpam-3363	372	15	101	101	NUM
ejpam-3363	372	16	-	-	SYM
ejpam-3363	372	17	117	117	NUM
ejpam-3363	372	18	114	114	NUM
ejpam-3363	372	19	e	e	NOUN
ejpam-3363	372	20	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-3363	372	21	n∑	n∑	NOUN
ejpam-3363	372	22	i=1	i=1	PROPN
ejpam-3363	372	23	{	{	PUNCT
ejpam-3363	372	24	fξi(wvi	fξi(wvi	NOUN
ejpam-3363	372	25	−wui)−	−wui)−	NOUN
ejpam-3363	372	26	f	f	PROPN
ejpam-3363	373	1	[	[	X
ejpam-3363	373	2	ui	ui	PROPN
ejpam-3363	373	3	,	,	PUNCT
ejpam-3363	373	4	vi	vi	PROPN
ejpam-3363	373	5	]	]	X
ejpam-3363	373	6	}	}	PUNCT
ejpam-3363	373	7	∥∥∥∥∥	∥∥∥∥∥	VERB
ejpam-3363	373	8	2	2	NUM
ejpam-3363	373	9	v	v	NOUN
ejpam-3363	373	10			NOUN
ejpam-3363	373	11	=	=	PUNCT
ejpam-3363	374	1	n∑	n∑	NOUN
ejpam-3363	374	2	i=1	i=1	PROPN
ejpam-3363	375	1	e	e	X
ejpam-3363	375	2	[	[	PUNCT
ejpam-3363	375	3	‖fξi(wvi	‖fξi(wvi	X
ejpam-3363	375	4	−wui)−	−wui)−	NOUN
ejpam-3363	375	5	f	f	PROPN
ejpam-3363	376	1	[	[	X
ejpam-3363	376	2	ui	ui	PROPN
ejpam-3363	376	3	,	,	PUNCT
ejpam-3363	376	4	vi]‖2v	vi]‖2v	X
ejpam-3363	376	5	]	]	PUNCT
ejpam-3363	376	6	<	<	X
ejpam-3363	376	7	ε	ε	PROPN
ejpam-3363	376	8	4	4	NUM
ejpam-3363	376	9	t	t	NOUN
ejpam-3363	376	10	n∑	n∑	X
ejpam-3363	376	11	i=1	i=1	PROPN
ejpam-3363	376	12	(	(	PUNCT
ejpam-3363	376	13	vi	vi	NOUN
ejpam-3363	376	14	−	−	PROPN
ejpam-3363	376	15	ui	ui	NOUN
ejpam-3363	376	16	)	)	PUNCT
ejpam-3363	376	17	≤	≤	PUNCT
ejpam-3363	376	18	ε	ε	PROPN
ejpam-3363	376	19	4	4	NUM
ejpam-3363	376	20	.	.	PUNCT
ejpam-3363	377	1	(	(	PUNCT
ejpam-3363	377	2	11	11	NUM
ejpam-3363	377	3	)	)	PUNCT
ejpam-3363	377	4	if	if	SCONJ
ejpam-3363	377	5	a	a	DET
ejpam-3363	377	6	=	=	NOUN
ejpam-3363	377	7	∅	∅	NOUN
ejpam-3363	377	8	,	,	PUNCT
ejpam-3363	377	9	then	then	ADV
ejpam-3363	377	10	we	we	PRON
ejpam-3363	377	11	are	be	AUX
ejpam-3363	377	12	done	do	VERB
ejpam-3363	377	13	.	.	PUNCT
ejpam-3363	377	14	suppose	suppose	VERB
ejpam-3363	377	15	that	that	SCONJ
ejpam-3363	377	16	a	a	DET
ejpam-3363	377	17	6=	6=	NUM
ejpam-3363	377	18	∅.	∅.	NOUN
ejpam-3363	377	19	let	let	VERB
ejpam-3363	377	20	ξ	ξ	PROPN
ejpam-3363	377	21	∈	∈	PROPN
ejpam-3363	377	22	a.	a.	NOUN
ejpam-3363	377	23	then	then	ADV
ejpam-3363	377	24	for	for	ADP
ejpam-3363	377	25	any	any	DET
ejpam-3363	377	26	[	[	X
ejpam-3363	377	27	u	u	NOUN
ejpam-3363	377	28	,	,	PUNCT
ejpam-3363	377	29	v	v	ADP
ejpam-3363	377	30	]	]	X
ejpam-3363	377	31	⊂	⊂	X
ejpam-3363	378	1	[	[	X
ejpam-3363	378	2	ξ	ξ	PROPN
ejpam-3363	378	3	,	,	PUNCT
ejpam-3363	378	4	t	t	X
ejpam-3363	378	5	]	]	PUNCT
ejpam-3363	378	6	,	,	PUNCT
ejpam-3363	378	7	e	e	X
ejpam-3363	378	8	[	[	PUNCT
ejpam-3363	378	9	‖fξ(wv	‖fξ(wv	NOUN
ejpam-3363	378	10	−wu)‖2v	−wu)‖2v	NOUN
ejpam-3363	378	11	]	]	X
ejpam-3363	378	12	=	=	PUNCT
ejpam-3363	378	13	(	(	PUNCT
ejpam-3363	378	14	v	v	NOUN
ejpam-3363	378	15	−	−	NOUN
ejpam-3363	378	16	u)e	u)e	ADJ
ejpam-3363	378	17	[	[	PUNCT
ejpam-3363	378	18	‖fξ‖2l2(uq	‖fξ‖2l2(uq	NUM
ejpam-3363	378	19	,	,	PUNCT
ejpam-3363	378	20	v	v	NOUN
ejpam-3363	378	21	)	)	PUNCT
ejpam-3363	378	22	]	]	PUNCT
ejpam-3363	378	23	.	.	PUNCT
ejpam-3363	379	1	let	let	VERB
ejpam-3363	379	2	gm	gm	PROPN
ejpam-3363	379	3	=	=	PUNCT
ejpam-3363	379	4	m∑	m∑	INTJ
ejpam-3363	379	5	k=1	k=1	PROPN
ejpam-3363	380	1	〈	〈	PROPN
ejpam-3363	380	2	fξ(wv	fξ(wv	NOUN
ejpam-3363	380	3	−wu	−wu	NUM
ejpam-3363	380	4	)	)	PUNCT
ejpam-3363	380	5	,	,	PUNCT
ejpam-3363	380	6	gk〉2	gk〉2	PROPN
ejpam-3363	380	7	,	,	PUNCT
ejpam-3363	380	8	where	where	SCONJ
ejpam-3363	380	9	{	{	PUNCT
ejpam-3363	380	10	gk	gk	NOUN
ejpam-3363	380	11	}	}	PUNCT
ejpam-3363	380	12	is	be	AUX
ejpam-3363	380	13	an	an	DET
ejpam-3363	380	14	onb	onb	ADJ
ejpam-3363	380	15	in	in	ADP
ejpam-3363	380	16	v	v	NOUN
ejpam-3363	380	17	.	.	PUNCT
ejpam-3363	381	1	since	since	SCONJ
ejpam-3363	381	2	gm	gm	PROPN
ejpam-3363	381	3	→	→	SYM
ejpam-3363	381	4	g	g	NOUN
ejpam-3363	381	5	:	:	PUNCT
ejpam-3363	381	6	=	=	SYM
ejpam-3363	381	7	∞∑	∞∑	NUM
ejpam-3363	381	8	k=1	k=1	PUNCT
ejpam-3363	381	9	〈	〈	PROPN
ejpam-3363	381	10	fξ(wv	fξ(wv	NOUN
ejpam-3363	381	11	−wu	−wu	NUM
ejpam-3363	381	12	)	)	PUNCT
ejpam-3363	381	13	,	,	PUNCT
ejpam-3363	381	14	gk〉2	gk〉2	VERB
ejpam-3363	381	15	as	as	ADP
ejpam-3363	381	16	m	m	PROPN
ejpam-3363	381	17	→	→	SYM
ejpam-3363	381	18	∞	∞	PROPN
ejpam-3363	381	19	and	and	CCONJ
ejpam-3363	381	20	gm	gm	PROPN
ejpam-3363	381	21	≤	≤	PROPN
ejpam-3363	381	22	gm+1	gm+1	X
ejpam-3363	381	23	,	,	PUNCT
ejpam-3363	381	24	by	by	ADP
ejpam-3363	381	25	the	the	DET
ejpam-3363	381	26	monotone	monotone	ADJ
ejpam-3363	381	27	convergence	convergence	NOUN
ejpam-3363	381	28	theorem	theorem	VERB
ejpam-3363	381	29	for	for	ADP
ejpam-3363	381	30	lebesgue	lebesgue	PROPN
ejpam-3363	381	31	integral	integral	ADJ
ejpam-3363	381	32	,	,	PUNCT
ejpam-3363	381	33	lim	lim	PROPN
ejpam-3363	381	34	m→∞	m→∞	NUM
ejpam-3363	381	35	e	e	NOUN
ejpam-3363	381	36	[	[	PUNCT
ejpam-3363	381	37	m∑	m∑	ADP
ejpam-3363	381	38	k=1	k=1	PROPN
ejpam-3363	381	39	〈	〈	PROPN
ejpam-3363	381	40	fξ(wv	fξ(wv	NOUN
ejpam-3363	381	41	−wu	−wu	NUM
ejpam-3363	381	42	)	)	PUNCT
ejpam-3363	381	43	,	,	PUNCT
ejpam-3363	381	44	gk〉2	gk〉2	PROPN
ejpam-3363	381	45	]	]	PUNCT
ejpam-3363	381	46	=	=	PUNCT
ejpam-3363	381	47	e	e	X
ejpam-3363	381	48	[	[	PUNCT
ejpam-3363	381	49	∞∑	∞∑	NUM
ejpam-3363	381	50	k=1	k=1	ADP
ejpam-3363	381	51	〈	〈	PROPN
ejpam-3363	381	52	fξ(wv	fξ(wv	NOUN
ejpam-3363	381	53	−wu	−wu	NUM
ejpam-3363	381	54	)	)	PUNCT
ejpam-3363	381	55	,	,	PUNCT
ejpam-3363	381	56	gk〉2	gk〉2	PROPN
ejpam-3363	381	57	]	]	PUNCT
ejpam-3363	382	1	=	=	PUNCT
ejpam-3363	382	2	e	e	X
ejpam-3363	382	3	[	[	PUNCT
ejpam-3363	382	4	‖fξ(wv	‖fξ(wv	NOUN
ejpam-3363	382	5	−wu)‖2v	−wu)‖2v	NOUN
ejpam-3363	382	6	]	]	X
ejpam-3363	382	7	<	<	X
ejpam-3363	382	8	∞.	∞.	PROPN
ejpam-3363	382	9	it	it	PRON
ejpam-3363	382	10	follows	follow	VERB
ejpam-3363	382	11	that	that	SCONJ
ejpam-3363	382	12	there	there	PRON
ejpam-3363	382	13	exists	exist	VERB
ejpam-3363	382	14	n	n	PRON
ejpam-3363	382	15	∈	∈	PROPN
ejpam-3363	382	16	n	n	PRON
ejpam-3363	382	17	such	such	ADJ
ejpam-3363	382	18	that	that	SCONJ
ejpam-3363	382	19	n	n	CCONJ
ejpam-3363	382	20	−	−	PROPN
ejpam-3363	382	21	1	1	NUM
ejpam-3363	382	22	≤	≤	NUM
ejpam-3363	382	23	e	e	X
ejpam-3363	382	24	[	[	PUNCT
ejpam-3363	382	25	‖fξ‖2l2(uq	‖fξ‖2l2(uq	NUM
ejpam-3363	382	26	,	,	PUNCT
ejpam-3363	382	27	v	v	NOUN
ejpam-3363	382	28	)	)	PUNCT
ejpam-3363	382	29	]	]	PUNCT
ejpam-3363	382	30	<	<	X
ejpam-3363	382	31	n	n	X
ejpam-3363	382	32	.	.	PUNCT
ejpam-3363	383	1	since	since	SCONJ
ejpam-3363	383	2	f	f	PROPN
ejpam-3363	383	3	is	be	AUX
ejpam-3363	383	4	ac2[0	ac2[0	ADJ
ejpam-3363	383	5	,	,	PUNCT
ejpam-3363	383	6	t	t	X
ejpam-3363	383	7	]	]	PUNCT
ejpam-3363	383	8	,	,	PUNCT
ejpam-3363	383	9	there	there	PRON
ejpam-3363	383	10	exists	exist	VERB
ejpam-3363	383	11	η	η	PROPN
ejpam-3363	383	12	>	>	X
ejpam-3363	383	13	0	0	PUNCT
ejpam-3363	383	14	with	with	ADP
ejpam-3363	383	15	η	η	PROPN
ejpam-3363	383	16	<	<	X
ejpam-3363	383	17	ε	ε	PROPN
ejpam-3363	383	18	4n	4n	VERB
ejpam-3363	383	19	such	such	ADJ
ejpam-3363	383	20	that	that	SCONJ
ejpam-3363	383	21	for	for	ADP
ejpam-3363	383	22	all	all	DET
ejpam-3363	383	23	finite	finite	ADJ
ejpam-3363	383	24	collection	collection	NOUN
ejpam-3363	383	25	{	{	PUNCT
ejpam-3363	384	1	[	[	X
ejpam-3363	384	2	uj	uj	X
ejpam-3363	384	3	,	,	PUNCT
ejpam-3363	384	4	vj	vj	X
ejpam-3363	384	5	]	]	X
ejpam-3363	384	6	}	}	PUNCT
ejpam-3363	384	7	pj=1	pj=1	NOUN
ejpam-3363	384	8	of	of	ADP
ejpam-3363	384	9	non	non	ADJ
ejpam-3363	384	10	-	-	ADJ
ejpam-3363	384	11	overlapping	overlapping	ADJ
ejpam-3363	384	12	intervals	interval	NOUN
ejpam-3363	384	13	of	of	ADP
ejpam-3363	384	14	[	[	X
ejpam-3363	384	15	0	0	NUM
ejpam-3363	384	16	,	,	PUNCT
ejpam-3363	384	17	t	t	X
ejpam-3363	384	18	]	]	PUNCT
ejpam-3363	384	19	with	with	ADP
ejpam-3363	384	20	∑p	∑p	PROPN
ejpam-3363	384	21	j=1(vj	j=1(vj	NOUN
ejpam-3363	385	1	−	−	PROPN
ejpam-3363	385	2	uj	uj	PROPN
ejpam-3363	385	3	)	)	PUNCT
ejpam-3363	385	4	<	<	X
ejpam-3363	385	5	η	η	PROPN
ejpam-3363	385	6	,	,	PUNCT
ejpam-3363	385	7	we	we	PRON
ejpam-3363	385	8	have	have	VERB
ejpam-3363	385	9	e	e	X
ejpam-3363	385	10	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ejpam-3363	385	11	p∑	p∑	X
ejpam-3363	386	1	j=1	j=1	NOUN
ejpam-3363	386	2	f	f	PROPN
ejpam-3363	387	1	[	[	X
ejpam-3363	387	2	uj	uj	PROPN
ejpam-3363	387	3	,	,	PUNCT
ejpam-3363	387	4	vj	vj	X
ejpam-3363	387	5	]	]	PUNCT
ejpam-3363	387	6	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-3363	387	7	2	2	NUM
ejpam-3363	387	8	v	v	NOUN
ejpam-3363	387	9			NOUN
ejpam-3363	387	10	<	<	X
ejpam-3363	387	11	ε	ε	PROPN
ejpam-3363	387	12	4	4	NUM
ejpam-3363	387	13	.	.	PUNCT
ejpam-3363	388	1	since	since	SCONJ
ejpam-3363	388	2	leb(a	leb(a	PROPN
ejpam-3363	388	3	)	)	PUNCT
ejpam-3363	388	4	=	=	SYM
ejpam-3363	388	5	0	0	NUM
ejpam-3363	388	6	,	,	PUNCT
ejpam-3363	388	7	there	there	PRON
ejpam-3363	388	8	exists	exist	VERB
ejpam-3363	388	9	an	an	DET
ejpam-3363	388	10	open	open	ADJ
ejpam-3363	388	11	set	set	NOUN
ejpam-3363	388	12	o	o	NOUN
ejpam-3363	388	13	containing	contain	VERB
ejpam-3363	388	14	a	a	DET
ejpam-3363	388	15	such	such	ADJ
ejpam-3363	388	16	that	that	SCONJ
ejpam-3363	388	17	leb(o	leb(o	PROPN
ejpam-3363	388	18	)	)	PUNCT
ejpam-3363	388	19	<	<	X
ejpam-3363	388	20	η	η	PROPN
ejpam-3363	388	21	.	.	PROPN
ejpam-3363	388	22	hence	hence	ADV
ejpam-3363	388	23	,	,	PUNCT
ejpam-3363	388	24	for	for	ADP
ejpam-3363	388	25	all	all	PRON
ejpam-3363	388	26	ξ	ξ	PROPN
ejpam-3363	388	27	∈	∈	PROPN
ejpam-3363	388	28	a	a	DET
ejpam-3363	388	29	⊆	⊆	NUM
ejpam-3363	388	30	o.	o.	NOUN
ejpam-3363	388	31	thus	thus	ADV
ejpam-3363	388	32	,	,	PUNCT
ejpam-3363	388	33	there	there	PRON
ejpam-3363	388	34	exists	exist	VERB
ejpam-3363	388	35	δ2(ξ	δ2(ξ	NUM
ejpam-3363	388	36	)	)	PUNCT
ejpam-3363	388	37	>	>	X
ejpam-3363	388	38	0	0	NUM
ejpam-3363	389	1	such	such	ADJ
ejpam-3363	389	2	that	that	SCONJ
ejpam-3363	390	1	[	[	X
ejpam-3363	390	2	ξi	ξi	NOUN
ejpam-3363	390	3	,	,	PUNCT
ejpam-3363	390	4	ξi	ξi	PROPN
ejpam-3363	390	5	+	+	NOUN
ejpam-3363	390	6	δ2(ξ	δ2(ξ	NUM
ejpam-3363	390	7	)	)	PUNCT
ejpam-3363	390	8	]	]	PUNCT
ejpam-3363	391	1	⊂	⊂	PROPN
ejpam-3363	391	2	o.	o.	PROPN
ejpam-3363	391	3	let	let	VERB
ejpam-3363	391	4	d2	d2	PROPN
ejpam-3363	391	5	=	=	PRON
ejpam-3363	391	6	{	{	PUNCT
ejpam-3363	391	7	(	(	PUNCT
ejpam-3363	391	8	[	[	X
ejpam-3363	391	9	u	u	NOUN
ejpam-3363	391	10	,	,	PUNCT
ejpam-3363	391	11	v	v	ADP
ejpam-3363	391	12	]	]	X
ejpam-3363	391	13	,	,	PUNCT
ejpam-3363	391	14	ξ	ξ	X
ejpam-3363	391	15	)	)	PUNCT
ejpam-3363	391	16	}	}	PUNCT
ejpam-3363	391	17	be	be	AUX
ejpam-3363	391	18	a	a	PRON
ejpam-3363	391	19	δ	δ	NOUN
ejpam-3363	391	20	-	-	PUNCT
ejpam-3363	391	21	fine	fine	NOUN
ejpam-3363	391	22	belated	belate	VERB
ejpam-3363	391	23	mcshane	mcshane	PROPN
ejpam-3363	391	24	partial	partial	ADJ
ejpam-3363	391	25	division	division	NOUN
ejpam-3363	391	26	such	such	ADJ
ejpam-3363	391	27	that	that	SCONJ
ejpam-3363	391	28	ξ	ξ	PROPN
ejpam-3363	391	29	∈	∈	PROPN
ejpam-3363	391	30	a.	a.	NOUN
ejpam-3363	391	31	then	then	ADV
ejpam-3363	391	32	,	,	PUNCT
ejpam-3363	391	33	(	(	PUNCT
ejpam-3363	391	34	d2	d2	PROPN
ejpam-3363	391	35	)	)	PUNCT
ejpam-3363	391	36	∑	∑	PUNCT
ejpam-3363	391	37	(	(	PUNCT
ejpam-3363	391	38	v	v	ADP
ejpam-3363	391	39	−	−	PROPN
ejpam-3363	391	40	u	u	NOUN
ejpam-3363	391	41	)	)	PUNCT
ejpam-3363	391	42	≤	≤	NOUN
ejpam-3363	391	43	leb(o	leb(o	PROPN
ejpam-3363	391	44	)	)	PUNCT
ejpam-3363	391	45	<	<	X
ejpam-3363	391	46	η	η	PROPN
ejpam-3363	391	47	.	.	PROPN
ejpam-3363	391	48	then	then	ADV
ejpam-3363	391	49	by	by	ADP
ejpam-3363	391	50	lemma	lemma	PROPN
ejpam-3363	391	51	3	3	NUM
ejpam-3363	391	52	,	,	PUNCT
ejpam-3363	391	53	j.d	j.d	PROPN
ejpam-3363	391	54	.	.	PROPN
ejpam-3363	391	55	cagubcob	cagubcob	PROPN
ejpam-3363	391	56	,	,	PUNCT
ejpam-3363	391	57	m.	m.	NOUN
ejpam-3363	391	58	labendia	labendia	PROPN
ejpam-3363	391	59	/	/	SYM
ejpam-3363	391	60	eur	eur	PROPN
ejpam-3363	391	61	.	.	PUNCT
ejpam-3363	392	1	j.	j.	PROPN
ejpam-3363	392	2	pure	pure	PROPN
ejpam-3363	392	3	appl	appl	PROPN
ejpam-3363	392	4	.	.	PROPN
ejpam-3363	392	5	math	math	PROPN
ejpam-3363	392	6	,	,	PUNCT
ejpam-3363	392	7	12	12	NUM
ejpam-3363	392	8	(	(	PUNCT
ejpam-3363	392	9	1	1	NUM
ejpam-3363	392	10	)	)	PUNCT
ejpam-3363	392	11	(	(	PUNCT
ejpam-3363	392	12	2019	2019	NUM
ejpam-3363	392	13	)	)	PUNCT
ejpam-3363	392	14	,	,	PUNCT
ejpam-3363	392	15	101	101	NUM
ejpam-3363	392	16	-	-	SYM
ejpam-3363	392	17	117	117	NUM
ejpam-3363	392	18	115	115	NUM
ejpam-3363	392	19	e	e	NOUN
ejpam-3363	392	20	[	[	X
ejpam-3363	392	21	∥∥∥(d2	∥∥∥(d2	NOUN
ejpam-3363	392	22	)	)	PUNCT
ejpam-3363	392	23	∑	∑	PUNCT
ejpam-3363	392	24	{	{	PUNCT
ejpam-3363	392	25	fξ(wv	fξ(wv	VERB
ejpam-3363	392	26	−wu)−	−wu)−	ADP
ejpam-3363	392	27	f	f	NOUN
ejpam-3363	392	28	[	[	X
ejpam-3363	392	29	u	u	NOUN
ejpam-3363	392	30	,	,	PUNCT
ejpam-3363	392	31	v	v	NOUN
ejpam-3363	392	32	]	]	X
ejpam-3363	392	33	}	}	PUNCT
ejpam-3363	392	34	∥∥∥2	∥∥∥2	NOUN
ejpam-3363	392	35	v	v	NOUN
ejpam-3363	392	36	]	]	X
ejpam-3363	392	37	=	=	SYM
ejpam-3363	392	38	(	(	PUNCT
ejpam-3363	392	39	d2	d2	PROPN
ejpam-3363	392	40	)	)	PUNCT
ejpam-3363	392	41	∑	∑	PUNCT
ejpam-3363	392	42	e	e	X
ejpam-3363	392	43	[	[	PUNCT
ejpam-3363	392	44	‖fξ(wv	‖fξ(wv	ADJ
ejpam-3363	392	45	−wu)−	−wu)−	NOUN
ejpam-3363	392	46	f	f	NOUN
ejpam-3363	393	1	[	[	X
ejpam-3363	393	2	u	u	NOUN
ejpam-3363	393	3	,	,	PUNCT
ejpam-3363	393	4	v]‖2v	v]‖2v	X
ejpam-3363	393	5	]	]	PUNCT
ejpam-3363	393	6	≤	≤	NUM
ejpam-3363	393	7	2(d2	2(d2	NUM
ejpam-3363	393	8	)	)	PUNCT
ejpam-3363	393	9	∑	∑	PUNCT
ejpam-3363	393	10	e	e	X
ejpam-3363	393	11	[	[	PUNCT
ejpam-3363	393	12	‖fξ(wv	‖fξ(wv	NOUN
ejpam-3363	393	13	−wu)‖2v	−wu)‖2v	NOUN
ejpam-3363	393	14	]	]	X
ejpam-3363	393	15	+	+	NUM
ejpam-3363	393	16	2(d2	2(d2	NUM
ejpam-3363	393	17	)	)	PUNCT
ejpam-3363	393	18	∑	∑	PUNCT
ejpam-3363	393	19	e	e	X
ejpam-3363	393	20	[	[	PUNCT
ejpam-3363	393	21	‖f	‖f	ADP
ejpam-3363	393	22	[	[	X
ejpam-3363	393	23	u	u	NOUN
ejpam-3363	393	24	,	,	PUNCT
ejpam-3363	393	25	v]‖2v	v]‖2v	NOUN
ejpam-3363	393	26	]	]	PUNCT
ejpam-3363	393	27	=	=	SYM
ejpam-3363	393	28	2(d2	2(d2	NUM
ejpam-3363	393	29	)	)	PUNCT
ejpam-3363	393	30	∑	∑	PUNCT
ejpam-3363	393	31	(	(	PUNCT
ejpam-3363	393	32	v	v	NOUN
ejpam-3363	393	33	−	−	NOUN
ejpam-3363	393	34	u)e	u)e	ADJ
ejpam-3363	393	35	[	[	PUNCT
ejpam-3363	393	36	‖fξ‖2l2(uq	‖fξ‖2l2(uq	NUM
ejpam-3363	393	37	,	,	PUNCT
ejpam-3363	393	38	v	v	NOUN
ejpam-3363	393	39	)	)	PUNCT
ejpam-3363	393	40	]	]	PUNCT
ejpam-3363	394	1	+	+	CCONJ
ejpam-3363	394	2	2(d2	2(d2	NUM
ejpam-3363	394	3	)	)	PUNCT
ejpam-3363	394	4	∑	∑	PUNCT
ejpam-3363	394	5	e	e	X
ejpam-3363	394	6	[	[	PUNCT
ejpam-3363	394	7	‖f	‖f	ADP
ejpam-3363	394	8	[	[	X
ejpam-3363	394	9	u	u	NOUN
ejpam-3363	394	10	,	,	PUNCT
ejpam-3363	394	11	v]‖2v	v]‖2v	X
ejpam-3363	394	12	]	]	PUNCT
ejpam-3363	394	13	<	<	X
ejpam-3363	394	14	2n(d2	2n(d2	NUM
ejpam-3363	394	15	)	)	PUNCT
ejpam-3363	394	16	∑	∑	PUNCT
ejpam-3363	394	17	(	(	PUNCT
ejpam-3363	394	18	v	v	ADP
ejpam-3363	394	19	−	−	PROPN
ejpam-3363	394	20	u	u	NOUN
ejpam-3363	394	21	)	)	PUNCT
ejpam-3363	394	22	+	+	NUM
ejpam-3363	394	23	2(d2	2(d2	NUM
ejpam-3363	394	24	)	)	PUNCT
ejpam-3363	394	25	∑	∑	PUNCT
ejpam-3363	394	26	e	e	X
ejpam-3363	394	27	[	[	PUNCT
ejpam-3363	394	28	‖f	‖f	ADP
ejpam-3363	394	29	[	[	X
ejpam-3363	394	30	u	u	NOUN
ejpam-3363	394	31	,	,	PUNCT
ejpam-3363	394	32	v]‖2v	v]‖2v	NOUN
ejpam-3363	394	33	]	]	PUNCT
ejpam-3363	394	34	≤	≤	NUM
ejpam-3363	394	35	2n	2n	NUM
ejpam-3363	394	36	·	·	PUNCT
ejpam-3363	394	37	ε	ε	PROPN
ejpam-3363	394	38	4n	4n	X
ejpam-3363	394	39	+	+	CCONJ
ejpam-3363	394	40	2	2	NUM
ejpam-3363	394	41	·	·	PUNCT
ejpam-3363	394	42	ε	ε	PROPN
ejpam-3363	394	43	4	4	NUM
ejpam-3363	394	44	=	=	SYM
ejpam-3363	394	45	ε	ε	PROPN
ejpam-3363	394	46	.	.	PUNCT
ejpam-3363	394	47	(	(	PUNCT
ejpam-3363	394	48	12	12	NUM
ejpam-3363	394	49	)	)	PUNCT
ejpam-3363	394	50	let	let	VERB
ejpam-3363	394	51	d	d	NOUN
ejpam-3363	394	52	=	=	PRON
ejpam-3363	394	53	{	{	PUNCT
ejpam-3363	394	54	(	(	PUNCT
ejpam-3363	394	55	[	[	X
ejpam-3363	394	56	u	u	NOUN
ejpam-3363	394	57	,	,	PUNCT
ejpam-3363	394	58	v	v	ADP
ejpam-3363	394	59	]	]	X
ejpam-3363	394	60	,	,	PUNCT
ejpam-3363	394	61	ξ	ξ	X
ejpam-3363	394	62	)	)	PUNCT
ejpam-3363	394	63	}	}	PUNCT
ejpam-3363	394	64	be	be	AUX
ejpam-3363	394	65	a	a	DET
ejpam-3363	394	66	δ	δ	NOUN
ejpam-3363	394	67	-	-	PUNCT
ejpam-3363	394	68	fine	fine	NOUN
ejpam-3363	394	69	belated	belate	VERB
ejpam-3363	394	70	mcshane	mcshane	PROPN
ejpam-3363	394	71	partial	partial	ADJ
ejpam-3363	394	72	division	division	NOUN
ejpam-3363	394	73	of	of	ADP
ejpam-3363	394	74	[	[	X
ejpam-3363	394	75	0	0	NUM
ejpam-3363	394	76	,	,	PUNCT
ejpam-3363	394	77	t	t	X
ejpam-3363	394	78	]	]	PUNCT
ejpam-3363	394	79	.	.	PUNCT
ejpam-3363	395	1	then	then	ADV
ejpam-3363	395	2	using	use	VERB
ejpam-3363	395	3	(	(	PUNCT
ejpam-3363	395	4	11	11	NUM
ejpam-3363	395	5	)	)	PUNCT
ejpam-3363	395	6	and	and	CCONJ
ejpam-3363	395	7	(	(	PUNCT
ejpam-3363	395	8	12	12	NUM
ejpam-3363	395	9	)	)	PUNCT
ejpam-3363	395	10	,	,	PUNCT
ejpam-3363	395	11	we	we	PRON
ejpam-3363	395	12	have	have	VERB
ejpam-3363	395	13	e	e	NOUN
ejpam-3363	395	14	[	[	X
ejpam-3363	395	15	∥∥∥(d	∥∥∥(d	X
ejpam-3363	395	16	)	)	PUNCT
ejpam-3363	395	17	∑	∑	PUNCT
ejpam-3363	395	18	{	{	PUNCT
ejpam-3363	395	19	fξ(wv	fξ(wv	VERB
ejpam-3363	395	20	−wu)−	−wu)−	ADP
ejpam-3363	395	21	f	f	NOUN
ejpam-3363	396	1	[	[	X
ejpam-3363	396	2	u	u	NOUN
ejpam-3363	396	3	,	,	PUNCT
ejpam-3363	396	4	v	v	NOUN
ejpam-3363	396	5	]	]	X
ejpam-3363	396	6	}	}	PUNCT
ejpam-3363	396	7	∥∥∥2	∥∥∥2	NOUN
ejpam-3363	396	8	v	v	ADP
ejpam-3363	396	9	]	]	PUNCT
ejpam-3363	396	10	≤	≤	NUM
ejpam-3363	396	11	2e	2e	X
ejpam-3363	396	12	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-3363	396	13	∑	∑	ADV
ejpam-3363	396	14	ξ∈ac	ξ∈ac	PROPN
ejpam-3363	396	15	{	{	PUNCT
ejpam-3363	396	16	fξ(wv	fξ(wv	VERB
ejpam-3363	396	17	−wu)−	−wu)−	ADP
ejpam-3363	396	18	f	f	PROPN
ejpam-3363	397	1	[	[	X
ejpam-3363	397	2	u	u	NOUN
ejpam-3363	397	3	,	,	PUNCT
ejpam-3363	397	4	v	v	NOUN
ejpam-3363	397	5	]	]	PUNCT
ejpam-3363	397	6	}	}	PUNCT
ejpam-3363	397	7	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-3363	397	8	2	2	NUM
ejpam-3363	397	9	v	v	NOUN
ejpam-3363	397	10			NOUN
ejpam-3363	397	11	+2e	+2e	PRON
ejpam-3363	397	12	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-3363	397	13	∑	∑	PUNCT
ejpam-3363	397	14	ξ∈a	ξ∈a	ADJ
ejpam-3363	397	15	{	{	PUNCT
ejpam-3363	397	16	fξ(wv	fξ(wv	VERB
ejpam-3363	397	17	−wu)−	−wu)−	ADP
ejpam-3363	397	18	f	f	NOUN
ejpam-3363	398	1	[	[	X
ejpam-3363	398	2	u	u	NOUN
ejpam-3363	398	3	,	,	PUNCT
ejpam-3363	398	4	v	v	NOUN
ejpam-3363	398	5	]	]	PUNCT
ejpam-3363	398	6	}	}	PUNCT
ejpam-3363	398	7	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-3363	398	8	2	2	NUM
ejpam-3363	398	9	v	v	NOUN
ejpam-3363	398	10			NOUN
ejpam-3363	398	11	<	<	X
ejpam-3363	398	12	2	2	NUM
ejpam-3363	398	13	(	(	PUNCT
ejpam-3363	398	14	ε	ε	PROPN
ejpam-3363	398	15	4	4	NUM
ejpam-3363	398	16	)	)	PUNCT
ejpam-3363	398	17	+	+	CCONJ
ejpam-3363	398	18	2	2	NUM
ejpam-3363	398	19	(	(	PUNCT
ejpam-3363	398	20	ε	ε	PROPN
ejpam-3363	398	21	4	4	NUM
ejpam-3363	398	22	)	)	PUNCT
ejpam-3363	398	23	=	=	SYM
ejpam-3363	398	24	ε	ε	PROPN
ejpam-3363	398	25	2	2	NUM
ejpam-3363	398	26	+	+	CCONJ
ejpam-3363	398	27	ε	ε	PROPN
ejpam-3363	398	28	2	2	NUM
ejpam-3363	398	29	=	=	SYM
ejpam-3363	398	30	ε	ε	PROPN
ejpam-3363	398	31	.	.	PUNCT
ejpam-3363	398	32	by	by	ADP
ejpam-3363	398	33	theorem	theorem	NOUN
ejpam-3363	398	34	2	2	NUM
ejpam-3363	398	35	,	,	PUNCT
ejpam-3363	398	36	f	f	PROPN
ejpam-3363	398	37	∈	∈	PROPN
ejpam-3363	398	38	λim	λim	X
ejpam-3363	398	39	and	and	CCONJ
ejpam-3363	398	40	f	f	X
ejpam-3363	399	1	[	[	X
ejpam-3363	399	2	u	u	NOUN
ejpam-3363	399	3	,	,	PUNCT
ejpam-3363	399	4	v	v	NOUN
ejpam-3363	399	5	]	]	PUNCT
ejpam-3363	399	6	:	:	PUNCT
ejpam-3363	399	7	=	=	SYM
ejpam-3363	399	8	(	(	PUNCT
ejpam-3363	399	9	i	i	NOUN
ejpam-3363	399	10	m	m	VERB
ejpam-3363	399	11	)	)	PUNCT
ejpam-3363	399	12	∫	∫	PROPN
ejpam-3363	400	1	v	v	NUM
ejpam-3363	400	2	u	u	PROPN
ejpam-3363	400	3	fs	fs	ADP
ejpam-3363	400	4	dws	dws	PROPN
ejpam-3363	400	5	for	for	ADP
ejpam-3363	400	6	all	all	DET
ejpam-3363	400	7	[	[	X
ejpam-3363	400	8	u	u	NOUN
ejpam-3363	400	9	,	,	PUNCT
ejpam-3363	400	10	v	v	ADP
ejpam-3363	400	11	]	]	X
ejpam-3363	400	12	⊂	⊂	PROPN
ejpam-3363	401	1	[	[	X
ejpam-3363	401	2	0	0	NUM
ejpam-3363	401	3	,	,	PUNCT
ejpam-3363	401	4	t	t	X
ejpam-3363	401	5	]	]	PUNCT
ejpam-3363	401	6	.	.	PUNCT
ejpam-3363	402	1	combining	combine	VERB
ejpam-3363	402	2	theorem	theorem	ADJ
ejpam-3363	402	3	1	1	NUM
ejpam-3363	402	4	,	,	PUNCT
ejpam-3363	402	5	theorem	theorem	VERB
ejpam-3363	402	6	3	3	NUM
ejpam-3363	402	7	,	,	PUNCT
ejpam-3363	402	8	and	and	CCONJ
ejpam-3363	402	9	theorem	theorem	VERB
ejpam-3363	402	10	4	4	NUM
ejpam-3363	402	11	,	,	PUNCT
ejpam-3363	402	12	we	we	PRON
ejpam-3363	402	13	get	get	VERB
ejpam-3363	402	14	the	the	DET
ejpam-3363	402	15	following	follow	VERB
ejpam-3363	402	16	result	result	NOUN
ejpam-3363	402	17	,	,	PUNCT
ejpam-3363	402	18	which	which	PRON
ejpam-3363	402	19	is	be	AUX
ejpam-3363	402	20	referred	refer	VERB
ejpam-3363	402	21	to	to	ADP
ejpam-3363	402	22	as	as	ADP
ejpam-3363	402	23	the	the	DET
ejpam-3363	402	24	fundamental	fundamental	ADJ
ejpam-3363	402	25	theorem	theorem	NOUN
ejpam-3363	402	26	or	or	CCONJ
ejpam-3363	402	27	the	the	DET
ejpam-3363	402	28	descriptive	descriptive	ADJ
ejpam-3363	402	29	definition	definition	NOUN
ejpam-3363	402	30	of	of	ADP
ejpam-3363	402	31	the	the	DET
ejpam-3363	402	32	itô-mcshane	itô-mcshane	NOUN
ejpam-3363	402	33	integral	integral	ADJ
ejpam-3363	402	34	for	for	ADP
ejpam-3363	402	35	the	the	DET
ejpam-3363	402	36	hilbert	hilbert	NOUN
ejpam-3363	402	37	-	-	PUNCT
ejpam-3363	402	38	schmidt	schmidt	VERB
ejpam-3363	402	39	-	-	PUNCT
ejpam-3363	402	40	valued	value	VERB
ejpam-3363	402	41	stochastic	stochastic	ADJ
ejpam-3363	402	42	process	process	NOUN
ejpam-3363	402	43	.	.	PUNCT
ejpam-3363	403	1	theorem	theorem	NOUN
ejpam-3363	403	2	5	5	NUM
ejpam-3363	403	3	.	.	PUNCT
ejpam-3363	404	1	let	let	VERB
ejpam-3363	404	2	f	f	NOUN
ejpam-3363	404	3	:	:	PUNCT
ejpam-3363	405	1	[	[	X
ejpam-3363	405	2	0	0	NUM
ejpam-3363	405	3	,	,	PUNCT
ejpam-3363	405	4	t	t	X
ejpam-3363	405	5	]	]	PUNCT
ejpam-3363	405	6	×	×	PROPN
ejpam-3363	405	7	ω	ω	PROPN
ejpam-3363	405	8	→	→	SYM
ejpam-3363	405	9	l(u	l(u	PROPN
ejpam-3363	405	10	,	,	PUNCT
ejpam-3363	405	11	v	v	NOUN
ejpam-3363	405	12	)	)	PUNCT
ejpam-3363	405	13	be	be	AUX
ejpam-3363	405	14	an	an	DET
ejpam-3363	405	15	adapted	adapt	VERB
ejpam-3363	405	16	process	process	NOUN
ejpam-3363	405	17	.	.	PUNCT
ejpam-3363	406	1	then	then	ADV
ejpam-3363	406	2	f	f	PROPN
ejpam-3363	406	3	∈	∈	PROPN
ejpam-3363	406	4	λim	λim	VERB
ejpam-3363	407	1	if	if	SCONJ
ejpam-3363	407	2	and	and	CCONJ
ejpam-3363	407	3	only	only	ADV
ejpam-3363	407	4	if	if	SCONJ
ejpam-3363	407	5	there	there	PRON
ejpam-3363	407	6	exists	exist	VERB
ejpam-3363	407	7	an	an	DET
ejpam-3363	407	8	ac2[0	ac2[0	NOUN
ejpam-3363	407	9	,	,	PUNCT
ejpam-3363	407	10	t	t	PROPN
ejpam-3363	407	11	]	]	PUNCT
ejpam-3363	407	12	function	function	NOUN
ejpam-3363	408	1	f	f	NOUN
ejpam-3363	408	2	:	:	PUNCT
ejpam-3363	408	3	j	j	PROPN
ejpam-3363	408	4	×	×	PROPN
ejpam-3363	408	5	ω	ω	PROPN
ejpam-3363	408	6	→	→	SYM
ejpam-3363	408	7	v	v	PROPN
ejpam-3363	408	8	that	that	PRON
ejpam-3363	408	9	satisfies	satisfy	VERB
ejpam-3363	408	10	the	the	DET
ejpam-3363	408	11	orthogonal	orthogonal	ADJ
ejpam-3363	408	12	increment	increment	NOUN
ejpam-3363	408	13	property	property	NOUN
ejpam-3363	408	14	and	and	CCONJ
ejpam-3363	408	15	dft	dft	NOUN
ejpam-3363	408	16	=	=	SYM
ejpam-3363	408	17	ft	ft	PROPN
ejpam-3363	408	18	a.e	a.e	PROPN
ejpam-3363	408	19	.	.	PROPN
ejpam-3363	408	20	on	on	ADP
ejpam-3363	408	21	[	[	X
ejpam-3363	408	22	0	0	NUM
ejpam-3363	408	23	,	,	PUNCT
ejpam-3363	408	24	t	t	NOUN
ejpam-3363	408	25	)	)	PUNCT
ejpam-3363	408	26	.	.	PUNCT
ejpam-3363	409	1	5	5	X
ejpam-3363	409	2	.	.	X
ejpam-3363	409	3	conclusion	conclusion	NOUN
ejpam-3363	409	4	and	and	CCONJ
ejpam-3363	409	5	recommendation	recommendation	NOUN
ejpam-3363	409	6	in	in	ADP
ejpam-3363	409	7	this	this	DET
ejpam-3363	409	8	paper	paper	NOUN
ejpam-3363	409	9	,	,	PUNCT
ejpam-3363	409	10	we	we	PRON
ejpam-3363	409	11	formulate	formulate	VERB
ejpam-3363	409	12	an	an	DET
ejpam-3363	409	13	equivalent	equivalent	ADJ
ejpam-3363	409	14	definition	definition	NOUN
ejpam-3363	409	15	of	of	ADP
ejpam-3363	409	16	the	the	DET
ejpam-3363	409	17	itô-mcshane	itô-mcshane	NOUN
ejpam-3363	409	18	integral	integral	ADJ
ejpam-3363	409	19	of	of	ADP
ejpam-3363	409	20	a	a	DET
ejpam-3363	409	21	operator	operator	NOUN
ejpam-3363	409	22	-	-	PUNCT
ejpam-3363	409	23	valued	value	VERB
ejpam-3363	409	24	stochastic	stochastic	ADJ
ejpam-3363	409	25	process	process	NOUN
ejpam-3363	409	26	with	with	ADP
ejpam-3363	409	27	respect	respect	NOUN
ejpam-3363	409	28	to	to	ADP
ejpam-3363	409	29	a	a	DET
ejpam-3363	409	30	hilbert	hilbert	NOUN
ejpam-3363	409	31	space	space	NOUN
ejpam-3363	409	32	-	-	PUNCT
ejpam-3363	409	33	valued	value	VERB
ejpam-3363	409	34	q	q	ADJ
ejpam-3363	409	35	-	-	PUNCT
ejpam-3363	409	36	wiener	wiener	NOUN
ejpam-3363	409	37	references	reference	NOUN
ejpam-3363	409	38	116	116	NUM
ejpam-3363	409	39	process	process	NOUN
ejpam-3363	409	40	using	use	VERB
ejpam-3363	409	41	the	the	DET
ejpam-3363	409	42	concept	concept	NOUN
ejpam-3363	409	43	of	of	ADP
ejpam-3363	409	44	belated	belate	VERB
ejpam-3363	409	45	mcshane	mcshane	PROPN
ejpam-3363	409	46	derivative	derivative	NOUN
ejpam-3363	409	47	and	and	CCONJ
ejpam-3363	409	48	ac2[0	ac2[0	ADJ
ejpam-3363	409	49	,	,	PUNCT
ejpam-3363	409	50	t	t	PROPN
ejpam-3363	409	51	]	]	PUNCT
ejpam-3363	409	52	-property	-property	PROPN
ejpam-3363	409	53	,	,	PUNCT
ejpam-3363	409	54	a	a	DET
ejpam-3363	409	55	version	version	NOUN
ejpam-3363	409	56	of	of	ADP
ejpam-3363	409	57	absolute	absolute	ADJ
ejpam-3363	409	58	continuity	continuity	NOUN
ejpam-3363	409	59	.	.	PUNCT
ejpam-3363	410	1	a	a	DET
ejpam-3363	410	2	worthwhile	worthwhile	ADJ
ejpam-3363	410	3	direction	direction	NOUN
ejpam-3363	410	4	for	for	ADP
ejpam-3363	410	5	further	further	ADJ
ejpam-3363	410	6	investigation	investigation	NOUN
ejpam-3363	410	7	is	be	AUX
ejpam-3363	410	8	to	to	PART
ejpam-3363	410	9	use	use	VERB
ejpam-3363	410	10	henstockkurzweil	henstockkurzweil	NOUN
ejpam-3363	410	11	approach	approach	NOUN
ejpam-3363	410	12	to	to	PART
ejpam-3363	410	13	define	define	VERB
ejpam-3363	410	14	the	the	DET
ejpam-3363	410	15	stochastic	stochastic	ADJ
ejpam-3363	410	16	integral	integral	ADJ
ejpam-3363	410	17	with	with	ADP
ejpam-3363	410	18	respect	respect	NOUN
ejpam-3363	410	19	to	to	ADP
ejpam-3363	410	20	a	a	DET
ejpam-3363	410	21	cylindrical	cylindrical	ADJ
ejpam-3363	410	22	wiener	wiener	NOUN
ejpam-3363	410	23	process	process	NOUN
ejpam-3363	410	24	.	.	PUNCT
ejpam-3363	411	1	acknowledgements	acknowledgement	NOUN
ejpam-3363	411	2	the	the	DET
ejpam-3363	411	3	authors	author	NOUN
ejpam-3363	411	4	would	would	AUX
ejpam-3363	411	5	like	like	VERB
ejpam-3363	411	6	to	to	PART
ejpam-3363	411	7	acknowledge	acknowledge	VERB
ejpam-3363	411	8	the	the	DET
ejpam-3363	411	9	financial	financial	ADJ
ejpam-3363	411	10	support	support	NOUN
ejpam-3363	411	11	from	from	ADP
ejpam-3363	411	12	the	the	DET
ejpam-3363	411	13	department	department	NOUN
ejpam-3363	411	14	of	of	ADP
ejpam-3363	411	15	science	science	NOUN
ejpam-3363	411	16	and	and	CCONJ
ejpam-3363	411	17	technology	technology	NOUN
ejpam-3363	411	18	-	-	PUNCT
ejpam-3363	411	19	accelerated	accelerate	VERB
ejpam-3363	411	20	science	science	NOUN
ejpam-3363	411	21	and	and	CCONJ
ejpam-3363	411	22	technology	technology	NOUN
ejpam-3363	411	23	human	human	ADJ
ejpam-3363	411	24	resource	resource	NOUN
ejpam-3363	411	25	development	development	NOUN
ejpam-3363	411	26	program	program	NOUN
ejpam-3363	411	27	(	(	PUNCT
ejpam-3363	411	28	dost	dost	NOUN
ejpam-3363	411	29	-	-	PUNCT
ejpam-3363	411	30	asthrdp	asthrdp	NOUN
ejpam-3363	411	31	)	)	PUNCT
ejpam-3363	411	32	and	and	CCONJ
ejpam-3363	411	33	to	to	PART
ejpam-3363	411	34	thank	thank	VERB
ejpam-3363	411	35	the	the	DET
ejpam-3363	411	36	unknown	unknown	ADJ
ejpam-3363	411	37	referee	referee	NOUN
ejpam-3363	411	38	for	for	ADP
ejpam-3363	411	39	reviewing	review	VERB
ejpam-3363	411	40	this	this	DET
ejpam-3363	411	41	paper	paper	NOUN
ejpam-3363	411	42	.	.	PUNCT
ejpam-3363	412	1	references	reference	NOUN
ejpam-3363	412	2	[	[	X
ejpam-3363	412	3	1	1	NUM
ejpam-3363	412	4	]	]	PUNCT
ejpam-3363	412	5	l.	l.	PROPN
ejpam-3363	412	6	gawarecki	gawarecki	PROPN
ejpam-3363	412	7	and	and	CCONJ
ejpam-3363	412	8	v.	v.	ADP
ejpam-3363	412	9	mandrekar	mandrekar	PROPN
ejpam-3363	412	10	.	.	PUNCT
ejpam-3363	413	1	stochastic	stochastic	ADJ
ejpam-3363	413	2	differential	differential	ADJ
ejpam-3363	413	3	equations	equation	NOUN
ejpam-3363	413	4	in	in	ADP
ejpam-3363	413	5	infinite	infinite	ADJ
ejpam-3363	413	6	dimensions	dimension	NOUN
ejpam-3363	413	7	with	with	ADP
ejpam-3363	413	8	applications	application	NOUN
ejpam-3363	413	9	to	to	PART
ejpam-3363	413	10	stochastic	stochastic	VERB
ejpam-3363	413	11	partial	partial	ADJ
ejpam-3363	413	12	differential	differential	NOUN
ejpam-3363	413	13	equations	equation	NOUN
ejpam-3363	413	14	.	.	PUNCT
ejpam-3363	414	1	springer	springer	NOUN
ejpam-3363	414	2	,	,	PUNCT
ejpam-3363	414	3	berlin	berlin	PROPN
ejpam-3363	414	4	,	,	PUNCT
ejpam-3363	414	5	2011	2011	NUM
ejpam-3363	414	6	.	.	PUNCT
ejpam-3363	415	1	[	[	X
ejpam-3363	415	2	2	2	NUM
ejpam-3363	415	3	]	]	PUNCT
ejpam-3363	415	4	r.	r.	PROPN
ejpam-3363	415	5	a.	a.	PROPN
ejpam-3363	415	6	gordon	gordon	PROPN
ejpam-3363	415	7	.	.	PUNCT
ejpam-3363	416	1	the	the	DET
ejpam-3363	416	2	integrals	integral	NOUN
ejpam-3363	416	3	of	of	ADP
ejpam-3363	416	4	lebesgue	lebesgue	NOUN
ejpam-3363	416	5	,	,	PUNCT
ejpam-3363	416	6	denjoy	denjoy	PROPN
ejpam-3363	416	7	,	,	PUNCT
ejpam-3363	416	8	perron	perron	PROPN
ejpam-3363	416	9	and	and	CCONJ
ejpam-3363	416	10	henstock	henstock	PROPN
ejpam-3363	416	11	.	.	PUNCT
ejpam-3363	417	1	american	american	PROPN
ejpam-3363	417	2	mathematical	mathematical	PROPN
ejpam-3363	417	3	society	society	NOUN
ejpam-3363	417	4	,	,	PUNCT
ejpam-3363	417	5	1994	1994	NUM
ejpam-3363	417	6	.	.	PUNCT
ejpam-3363	418	1	[	[	X
ejpam-3363	418	2	3	3	X
ejpam-3363	418	3	]	]	X
ejpam-3363	418	4	r.	r.	PROPN
ejpam-3363	418	5	henstock	henstock	PROPN
ejpam-3363	418	6	.	.	PUNCT
ejpam-3363	419	1	lectures	lecture	NOUN
ejpam-3363	419	2	on	on	ADP
ejpam-3363	419	3	the	the	DET
ejpam-3363	419	4	theory	theory	NOUN
ejpam-3363	419	5	of	of	ADP
ejpam-3363	419	6	integration	integration	NOUN
ejpam-3363	419	7	.	.	PUNCT
ejpam-3363	420	1	world	world	NOUN
ejpam-3363	420	2	scientific	scientific	PROPN
ejpam-3363	420	3	,	,	PUNCT
ejpam-3363	420	4	singapore	singapore	PROPN
ejpam-3363	420	5	,	,	PUNCT
ejpam-3363	420	6	1988	1988	NUM
ejpam-3363	420	7	.	.	PUNCT
ejpam-3363	421	1	[	[	X
ejpam-3363	421	2	4	4	X
ejpam-3363	421	3	]	]	PUNCT
ejpam-3363	421	4	j.	j.	PROPN
ejpam-3363	421	5	kurzweil	kurzweil	PROPN
ejpam-3363	421	6	.	.	PUNCT
ejpam-3363	421	7	henstock	henstock	PROPN
ejpam-3363	421	8	-	-	PUNCT
ejpam-3363	421	9	kurzweil	kurzweil	NOUN
ejpam-3363	421	10	integration	integration	NOUN
ejpam-3363	421	11	:	:	PUNCT
ejpam-3363	421	12	its	its	PRON
ejpam-3363	421	13	relation	relation	NOUN
ejpam-3363	421	14	to	to	ADP
ejpam-3363	421	15	topological	topological	ADJ
ejpam-3363	421	16	vector	vector	NOUN
ejpam-3363	421	17	spaces	space	NOUN
ejpam-3363	421	18	.	.	PUNCT
ejpam-3363	422	1	world	world	NOUN
ejpam-3363	422	2	scientific	scientific	PROPN
ejpam-3363	422	3	,	,	PUNCT
ejpam-3363	422	4	singapore	singapore	PROPN
ejpam-3363	422	5	,	,	PUNCT
ejpam-3363	422	6	2000	2000	NUM
ejpam-3363	422	7	.	.	PUNCT
ejpam-3363	423	1	[	[	X
ejpam-3363	423	2	5	5	X
ejpam-3363	423	3	]	]	PUNCT
ejpam-3363	423	4	m.	m.	NOUN
ejpam-3363	423	5	labendia	labendia	PROPN
ejpam-3363	423	6	and	and	CCONJ
ejpam-3363	423	7	j.	j.	PROPN
ejpam-3363	423	8	arcede	arcede	PROPN
ejpam-3363	423	9	.	.	PUNCT
ejpam-3363	424	1	a	a	DET
ejpam-3363	424	2	descriptive	descriptive	ADJ
ejpam-3363	424	3	definition	definition	NOUN
ejpam-3363	424	4	of	of	ADP
ejpam-3363	424	5	the	the	DET
ejpam-3363	424	6	itô-henstock	itô-henstock	NOUN
ejpam-3363	424	7	integral	integral	ADJ
ejpam-3363	424	8	for	for	ADP
ejpam-3363	424	9	the	the	DET
ejpam-3363	424	10	operator	operator	NOUN
ejpam-3363	424	11	-	-	PUNCT
ejpam-3363	424	12	valued	value	VERB
ejpam-3363	424	13	stochastic	stochastic	ADJ
ejpam-3363	424	14	process	process	NOUN
ejpam-3363	424	15	.	.	PUNCT
ejpam-3363	425	1	advances	advance	NOUN
ejpam-3363	425	2	in	in	ADP
ejpam-3363	425	3	operator	operator	NOUN
ejpam-3363	425	4	theory	theory	NOUN
ejpam-3363	425	5	,	,	PUNCT
ejpam-3363	425	6	4:406–418	4:406–418	NOUN
ejpam-3363	425	7	,	,	PUNCT
ejpam-3363	425	8	2019	2019	NUM
ejpam-3363	425	9	.	.	PUNCT
ejpam-3363	426	1	[	[	X
ejpam-3363	426	2	6	6	NUM
ejpam-3363	426	3	]	]	PUNCT
ejpam-3363	426	4	m.	m.	NOUN
ejpam-3363	426	5	labendia	labendia	PROPN
ejpam-3363	426	6	e.	e.	PROPN
ejpam-3363	426	7	de	de	PROPN
ejpam-3363	426	8	lara	lara	PROPN
ejpam-3363	426	9	-	-	PUNCT
ejpam-3363	426	10	tuprio	tuprio	PROPN
ejpam-3363	426	11	and	and	CCONJ
ejpam-3363	426	12	t.	t.	PROPN
ejpam-3363	426	13	r.	r.	PROPN
ejpam-3363	426	14	teng	teng	PROPN
ejpam-3363	426	15	.	.	PUNCT
ejpam-3363	427	1	itô-henstock	itô-henstock	PROPN
ejpam-3363	427	2	integral	integral	ADJ
ejpam-3363	427	3	and	and	CCONJ
ejpam-3363	427	4	itô	itô	PROPN
ejpam-3363	427	5	’s	’s	PART
ejpam-3363	427	6	formula	formula	NOUN
ejpam-3363	427	7	for	for	ADP
ejpam-3363	427	8	the	the	DET
ejpam-3363	427	9	operator	operator	NOUN
ejpam-3363	427	10	-	-	PUNCT
ejpam-3363	427	11	valued	value	VERB
ejpam-3363	427	12	stochastic	stochastic	ADJ
ejpam-3363	427	13	process	process	NOUN
ejpam-3363	427	14	.	.	PUNCT
ejpam-3363	428	1	mathematica	mathematica	PROPN
ejpam-3363	428	2	bohemica	bohemica	PROPN
ejpam-3363	428	3	,	,	PUNCT
ejpam-3363	428	4	143:135	143:135	NUM
ejpam-3363	428	5	–	–	PUNCT
ejpam-3363	428	6	160	160	NUM
ejpam-3363	428	7	,	,	PUNCT
ejpam-3363	428	8	2018	2018	NUM
ejpam-3363	428	9	.	.	PUNCT
ejpam-3363	429	1	[	[	X
ejpam-3363	429	2	7	7	X
ejpam-3363	429	3	]	]	X
ejpam-3363	429	4	p.	p.	NOUN
ejpam-3363	429	5	y.	y.	PROPN
ejpam-3363	429	6	lee	lee	PROPN
ejpam-3363	429	7	.	.	PUNCT
ejpam-3363	430	1	lanzhou	lanzhou	PROPN
ejpam-3363	430	2	lectures	lecture	VERB
ejpam-3363	430	3	on	on	ADP
ejpam-3363	430	4	henstock	henstock	NOUN
ejpam-3363	430	5	integration	integration	NOUN
ejpam-3363	430	6	.	.	PUNCT
ejpam-3363	431	1	world	world	NOUN
ejpam-3363	431	2	scientific	scientific	PROPN
ejpam-3363	431	3	,	,	PUNCT
ejpam-3363	431	4	singapore	singapore	PROPN
ejpam-3363	431	5	,	,	PUNCT
ejpam-3363	431	6	1989	1989	NUM
ejpam-3363	431	7	.	.	PUNCT
ejpam-3363	432	1	[	[	X
ejpam-3363	432	2	8	8	NUM
ejpam-3363	432	3	]	]	PUNCT
ejpam-3363	432	4	p.	p.	NOUN
ejpam-3363	432	5	y.	y.	PROPN
ejpam-3363	432	6	lee	lee	PROPN
ejpam-3363	432	7	and	and	CCONJ
ejpam-3363	432	8	r.	r.	PROPN
ejpam-3363	432	9	výborný.	výborný.	VERB
ejpam-3363	432	10	the	the	DET
ejpam-3363	432	11	integral	integral	ADJ
ejpam-3363	432	12	:	:	PUNCT
ejpam-3363	432	13	an	an	DET
ejpam-3363	432	14	easy	easy	ADJ
ejpam-3363	432	15	approach	approach	NOUN
ejpam-3363	432	16	after	after	ADP
ejpam-3363	432	17	kurzweil	kurzweil	PROPN
ejpam-3363	432	18	and	and	CCONJ
ejpam-3363	432	19	henstock	henstock	PROPN
ejpam-3363	432	20	.	.	PUNCT
ejpam-3363	433	1	cambridge	cambridge	PROPN
ejpam-3363	433	2	university	university	PROPN
ejpam-3363	433	3	press	press	PROPN
ejpam-3363	433	4	,	,	PUNCT
ejpam-3363	433	5	cambridge	cambridge	PROPN
ejpam-3363	433	6	,	,	PUNCT
ejpam-3363	433	7	2000	2000	NUM
ejpam-3363	433	8	.	.	PUNCT
ejpam-3363	434	1	[	[	X
ejpam-3363	434	2	9	9	NUM
ejpam-3363	434	3	]	]	PUNCT
ejpam-3363	434	4	t.	t.	PROPN
ejpam-3363	434	5	y.	y.	PROPN
ejpam-3363	434	6	lee	lee	PROPN
ejpam-3363	434	7	.	.	PUNCT
ejpam-3363	434	8	henstock	henstock	PROPN
ejpam-3363	434	9	-	-	PUNCT
ejpam-3363	434	10	kurzweil	kurzweil	NOUN
ejpam-3363	434	11	integration	integration	NOUN
ejpam-3363	434	12	on	on	ADP
ejpam-3363	434	13	euclidean	euclidean	ADJ
ejpam-3363	434	14	spaces	space	NOUN
ejpam-3363	434	15	.	.	PUNCT
ejpam-3363	435	1	world	world	NOUN
ejpam-3363	435	2	scientific	scientific	PROPN
ejpam-3363	435	3	,	,	PUNCT
ejpam-3363	435	4	singapore	singapore	PROPN
ejpam-3363	435	5	,	,	PUNCT
ejpam-3363	435	6	2011	2011	NUM
ejpam-3363	435	7	.	.	PUNCT
ejpam-3363	436	1	[	[	X
ejpam-3363	436	2	10	10	NUM
ejpam-3363	436	3	]	]	X
ejpam-3363	436	4	e.	e.	PROPN
ejpam-3363	436	5	j.	j.	PROPN
ejpam-3363	436	6	mcshane	mcshane	PROPN
ejpam-3363	436	7	.	.	PUNCT
ejpam-3363	437	1	stochastic	stochastic	ADJ
ejpam-3363	437	2	integrals	integral	NOUN
ejpam-3363	437	3	and	and	CCONJ
ejpam-3363	437	4	stochastic	stochastic	ADJ
ejpam-3363	437	5	functional	functional	ADJ
ejpam-3363	437	6	equations	equation	NOUN
ejpam-3363	437	7	.	.	PUNCT
ejpam-3363	438	1	siam	siam	PROPN
ejpam-3363	438	2	j.	j.	PROPN
ejpam-3363	438	3	appl	appl	PROPN
ejpam-3363	438	4	.	.	PROPN
ejpam-3363	438	5	math	math	PROPN
ejpam-3363	438	6	.	.	PUNCT
ejpam-3363	438	7	,	,	PUNCT
ejpam-3363	439	1	17:287–306	17:287–306	NUM
ejpam-3363	439	2	,	,	PUNCT
ejpam-3363	439	3	1969	1969	NUM
ejpam-3363	439	4	.	.	PUNCT
ejpam-3363	440	1	references	reference	NOUN
ejpam-3363	440	2	117	117	NUM
ejpam-3363	441	1	[	[	X
ejpam-3363	441	2	11	11	NUM
ejpam-3363	441	3	]	]	PUNCT
ejpam-3363	441	4	z.	z.	PROPN
ejpam-3363	441	5	r.	r.	PROPN
ejpam-3363	441	6	pop	pop	PROPN
ejpam-3363	441	7	-	-	PUNCT
ejpam-3363	441	8	stojanovic	stojanovic	ADJ
ejpam-3363	441	9	.	.	PUNCT
ejpam-3363	442	1	on	on	ADP
ejpam-3363	442	2	mcshane	mcshane	PROPN
ejpam-3363	442	3	’s	’s	PART
ejpam-3363	442	4	belated	belate	VERB
ejpam-3363	442	5	stochastci	stochastci	NOUN
ejpam-3363	442	6	integral	integral	ADJ
ejpam-3363	442	7	.	.	PUNCT
ejpam-3363	443	1	siam	siam	PROPN
ejpam-3363	443	2	j.	j.	PROPN
ejpam-3363	443	3	appl	appl	PROPN
ejpam-3363	443	4	.	.	PROPN
ejpam-3363	443	5	math	math	PROPN
ejpam-3363	443	6	.	.	PUNCT
ejpam-3363	443	7	,	,	PUNCT
ejpam-3363	443	8	22:87–92	22:87–92	PROPN
ejpam-3363	443	9	,	,	PUNCT
ejpam-3363	443	10	1972	1972	NUM
ejpam-3363	443	11	.	.	PUNCT
ejpam-3363	444	1	[	[	X
ejpam-3363	444	2	12	12	NUM
ejpam-3363	444	3	]	]	X
ejpam-3363	444	4	c.	c.	NOUN
ejpam-3363	444	5	prévôt	prévôt	NOUN
ejpam-3363	444	6	and	and	CCONJ
ejpam-3363	444	7	m.	m.	NOUN
ejpam-3363	444	8	röckner	röckner	NOUN
ejpam-3363	444	9	.	.	PUNCT
ejpam-3363	445	1	a	a	DET
ejpam-3363	445	2	concise	concise	ADJ
ejpam-3363	445	3	course	course	NOUN
ejpam-3363	445	4	on	on	ADP
ejpam-3363	445	5	stochastic	stochastic	ADJ
ejpam-3363	445	6	partial	partial	ADJ
ejpam-3363	445	7	differential	differential	NOUN
ejpam-3363	445	8	equations	equation	NOUN
ejpam-3363	445	9	.	.	PUNCT
ejpam-3363	446	1	2007	2007	NUM
ejpam-3363	446	2	.	.	PUNCT
ejpam-3363	447	1	[	[	X
ejpam-3363	447	2	13	13	NUM
ejpam-3363	447	3	]	]	X
ejpam-3363	447	4	g.	g.	PROPN
ejpam-3363	447	5	da	da	PROPN
ejpam-3363	447	6	prato	prato	PROPN
ejpam-3363	447	7	and	and	CCONJ
ejpam-3363	447	8	j.	j.	PROPN
ejpam-3363	447	9	zabczyk	zabczyk	PROPN
ejpam-3363	447	10	.	.	PUNCT
ejpam-3363	448	1	stochastic	stochastic	ADJ
ejpam-3363	448	2	equations	equation	NOUN
ejpam-3363	448	3	in	in	ADP
ejpam-3363	448	4	infinite	infinite	ADJ
ejpam-3363	448	5	dimensions	dimension	NOUN
ejpam-3363	448	6	.	.	PUNCT
ejpam-3363	449	1	cambridge	cambridge	PROPN
ejpam-3363	449	2	university	university	PROPN
ejpam-3363	449	3	press	press	PROPN
ejpam-3363	449	4	,	,	PUNCT
ejpam-3363	449	5	cambridge	cambridge	PROPN
ejpam-3363	449	6	,	,	PUNCT
ejpam-3363	449	7	1992	1992	NUM
ejpam-3363	449	8	.	.	PUNCT
ejpam-3363	450	1	[	[	X
ejpam-3363	450	2	14	14	NUM
ejpam-3363	450	3	]	]	PUNCT
ejpam-3363	450	4	m.	m.	NOUN
ejpam-3363	450	5	reed	reed	PROPN
ejpam-3363	450	6	and	and	CCONJ
ejpam-3363	450	7	b.	b.	PROPN
ejpam-3363	450	8	simon	simon	PROPN
ejpam-3363	450	9	.	.	PUNCT
ejpam-3363	451	1	methods	method	NOUN
ejpam-3363	451	2	of	of	ADP
ejpam-3363	451	3	modern	modern	ADJ
ejpam-3363	451	4	mathematical	mathematical	ADJ
ejpam-3363	451	5	physics	physics	NOUN
ejpam-3363	451	6	i	i	PRON
ejpam-3363	451	7	:	:	PUNCT
ejpam-3363	451	8	functional	functional	ADJ
ejpam-3363	451	9	analysis	analysis	NOUN
ejpam-3363	451	10	.	.	PUNCT
ejpam-3363	451	11	1980	1980	NUM
ejpam-3363	451	12	.	.	PUNCT
ejpam-3363	452	1	[	[	X
ejpam-3363	452	2	15	15	NUM
ejpam-3363	452	3	]	]	X
ejpam-3363	452	4	t.	t.	PROPN
ejpam-3363	452	5	l.	l.	PROPN
ejpam-3363	452	6	toh	toh	PROPN
ejpam-3363	452	7	and	and	CCONJ
ejpam-3363	452	8	t.	t.	PROPN
ejpam-3363	452	9	s.	s.	PROPN
ejpam-3363	452	10	chew	chew	VERB
ejpam-3363	452	11	.	.	PUNCT
ejpam-3363	453	1	the	the	DET
ejpam-3363	453	2	riemann	riemann	PROPN
ejpam-3363	453	3	approach	approach	NOUN
ejpam-3363	453	4	to	to	ADP
ejpam-3363	453	5	stochastic	stochastic	ADJ
ejpam-3363	453	6	integration	integration	NOUN
ejpam-3363	453	7	using	use	VERB
ejpam-3363	453	8	non	non	ADJ
ejpam-3363	453	9	-	-	ADJ
ejpam-3363	453	10	uniform	uniform	ADJ
ejpam-3363	453	11	meshes	mesh	NOUN
ejpam-3363	453	12	.	.	PUNCT
ejpam-3363	454	1	j.	j.	PROPN
ejpam-3363	454	2	math	math	PROPN
ejpam-3363	454	3	.	.	PUNCT
ejpam-3363	455	1	anal	anal	PROPN
ejpam-3363	455	2	.	.	PUNCT
ejpam-3363	456	1	appl	appl	PROPN
ejpam-3363	456	2	.	.	PROPN
ejpam-3363	456	3	,	,	PUNCT
ejpam-3363	456	4	280:133–147	280:133–147	NUM
ejpam-3363	456	5	,	,	PUNCT
ejpam-3363	456	6	2003	2003	NUM
ejpam-3363	456	7	.	.	PUNCT
ejpam-3363	457	1	[	[	X
ejpam-3363	457	2	16	16	NUM
ejpam-3363	457	3	]	]	PUNCT
ejpam-3363	457	4	t.	t.	PROPN
ejpam-3363	457	5	l.	l.	PROPN
ejpam-3363	457	6	toh	toh	PROPN
ejpam-3363	457	7	and	and	CCONJ
ejpam-3363	457	8	t.	t.	PROPN
ejpam-3363	457	9	s.	s.	PROPN
ejpam-3363	457	10	chew	chew	VERB
ejpam-3363	457	11	.	.	PUNCT
ejpam-3363	458	1	on	on	ADP
ejpam-3363	458	2	the	the	DET
ejpam-3363	458	3	henstock	henstock	NOUN
ejpam-3363	458	4	-	-	PUNCT
ejpam-3363	458	5	fubini	fubini	NOUN
ejpam-3363	458	6	theorem	theorem	NOUN
ejpam-3363	458	7	for	for	ADP
ejpam-3363	458	8	multiple	multiple	ADJ
ejpam-3363	458	9	stochastic	stochastic	ADJ
ejpam-3363	458	10	integrals	integral	NOUN
ejpam-3363	458	11	.	.	PUNCT
ejpam-3363	459	1	real	real	ADJ
ejpam-3363	459	2	anal	anal	PROPN
ejpam-3363	459	3	.	.	PUNCT
ejpam-3363	460	1	exchange	exchange	NOUN
ejpam-3363	460	2	,	,	PUNCT
ejpam-3363	460	3	30:295–310	30:295–310	NUM
ejpam-3363	460	4	,	,	PUNCT
ejpam-3363	460	5	2004	2004	NUM
ejpam-3363	460	6	-	-	SYM
ejpam-3363	460	7	2005	2005	NUM
ejpam-3363	460	8	.	.	PUNCT
ejpam-3363	461	1	[	[	X
ejpam-3363	461	2	17	17	NUM
ejpam-3363	461	3	]	]	PUNCT
ejpam-3363	461	4	t.	t.	PROPN
ejpam-3363	461	5	s.	s.	PROPN
ejpam-3363	461	6	chew	chew	VERB
ejpam-3363	461	7	t.	t.	PROPN
ejpam-3363	461	8	l.	l.	PROPN
ejpam-3363	461	9	toh	toh	PROPN
ejpam-3363	461	10	and	and	CCONJ
ejpam-3363	461	11	j.	j.	PROPN
ejpam-3363	461	12	y.	y.	PROPN
ejpam-3363	461	13	tay	tay	PROPN
ejpam-3363	461	14	.	.	PUNCT
ejpam-3363	462	1	the	the	DET
ejpam-3363	462	2	non	non	ADJ
ejpam-3363	462	3	-	-	ADJ
ejpam-3363	462	4	uniform	uniform	ADJ
ejpam-3363	462	5	riemann	riemann	PROPN
ejpam-3363	462	6	approach	approach	NOUN
ejpam-3363	462	7	to	to	ADP
ejpam-3363	462	8	itô	itô	PROPN
ejpam-3363	462	9	’s	’s	PART
ejpam-3363	462	10	integral	integral	ADJ
ejpam-3363	462	11	.	.	PUNCT
ejpam-3363	463	1	real	real	ADJ
ejpam-3363	463	2	anal	anal	PROPN
ejpam-3363	463	3	.	.	PUNCT
ejpam-3363	464	1	exchange	exchange	NOUN
ejpam-3363	464	2	,	,	PUNCT
ejpam-3363	464	3	27:495–514	27:495–514	NUM
ejpam-3363	464	4	,	,	PUNCT
ejpam-3363	464	5	2002	2002	NUM
ejpam-3363	464	6	-	-	SYM
ejpam-3363	464	7	2003	2003	NUM
ejpam-3363	464	8	.	.	PUNCT